chunky v0.13.0 Chunky.Sequence.OEIS.Core View Source
OEIS Core Sequences.
Available Sequences
Divisors and Factors
Core sequences dealing with divisors and factors of numbers, or the counting of divisors and factors. See Chunky.Sequence.OEIS.Factors for
non-core sequences of divisors and factors.
create_sequence_a000005/1- A000005 - Divisors of Ncreate_sequence_a000203/1- A000203 - Sum of Divisorscreate_sequence_a000396/1- A000396 - Perfect Numberscreate_sequence_a000593/1- A000593 - Sum of Odd Divisors of Ncreate_sequence_a001065/1- A001065 - Sum of proper divisors (Aliquot parts) of N.create_sequence_a001157/1- A001157 - Sum of squares of divisors of Ncreate_sequence_a001221/1- A001221 - Number of distinct primes dividing n (also called omega(n)).create_sequence_a001222/1- A001222 - Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n)).create_sequence_a001227/1- A001227 - Number of odd divisors of n.create_sequence_a006530/1- A006530 - Gpf(n): greatest prime dividing ncreate_sequence_a020639/1- A020639 - Lpf(n): least prime dividing ncreate_sequence_a074206/1- A074206 - Kalmár's [Kalmar's] problem: number of ordered factorizations of n.create_sequence_a001511/1- A001511 - The ruler function: 2^a(n) divides 2ncreate_sequence_a008683/1- A008683 - Möbius (or Moebius) function mu(n)create_sequence_a005100/1- A005100 - Deficient Numberscreate_sequence_a005101/1- A005101 - Abundant Numbers
Powers and Multiples
Core sequences for the powers and multiples of numbers. See Chunky.Sequence.OEIS.Multiples and Chunky.Sequence.OEIS.Powers for non-core
sequences of integer powers and multiples.
create_sequence_a000007/1- A000007 - The characteristic function of {0}: a(n) = 0^ncreate_sequence_a000079/1- A000079 - Powers of 2create_sequence_a000225/1- A000225 - a(n) = 2^n - 1create_sequence_a000244/1- A000244 - Powers of 3create_sequence_a000290/1- A000290 - The squares: a(n) = n^2create_sequence_a000302/1- A000302 - Powers of 4: a(n) = 4^ncreate_sequence_a000578/1- A000578 - The cubes: a(n) = n^3.create_sequence_a000583/1- A000583 - Fourth powers: a(n) = n^4.create_sequence_a000961/1- A000961 - Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1)create_sequence_a001481/1- A001481 - Numbers that are the sum of 2 squares.create_sequence_a002620/1- A002620 - Quarter-squares: floor(n/2)*ceiling(n/2). Equivalently, floor(n^2/4).create_sequence_a003418/1- A003418 - Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1.create_sequence_a005117/1- A005117 - Squarefree numbers: numbers that are not divisible by a square greater than 1
Representations and Patterns
Core sequences that depend on digit patterns or representations, particularly in specific bases. See Chunky.Sequence.OEIS.Repr for non-core
sequences of digit patterns and base dependent representations.
create_sequence_a000035/1- A000035 - Period 2: repeat [0, 1]; a(n) = n mod 2create_sequence_a000069/1- A000069 - Odious numbers: numbers with an odd number of 1's in their binary expansioncreate_sequence_a000120/1- A000120 - 1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n)create_sequence_a002113/1- A002113 - Palindromes in base 10.create_sequence_a002275/1- A002275 - Repunits: (10^n - 1)/9. Often denoted by R_n.create_sequence_a001969/1- A001969 - Evil numbers: numbers with an even number of 1's in their binary expansion.create_sequence_a070939/1- A070939 - Length of binary representation of n.create_sequence_a005811/1- A005811 - Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n.
Combinatorics
Core sequences for combinatorics and counting functions. See Chunky.Sequence.OEIS.Combinatorics for non-core sequences dealing with
combinatorics and counting functions.
create_sequence_a000001/1- A000001 - Number of groups of order ncreate_sequence_a000009/1- A000009 - Number of partitions of n into distinct partscreate_sequence_a000029/1- A000029 - Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets).create_sequence_a000031/1- A000031 - Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n.create_sequence_a000041/1- A000041 - Partition Numberscreate_sequence_a000048/1- A000048 - Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged.create_sequence_a000081/1- A000081 - Number of unlabeled rooted trees with n nodescreate_sequence_a000085/1- A000085 - Number of self-inverse permutations on n letters, also known as involutionscreate_sequence_a000105/1- A000105 - Number of free polyominoes (or square animals) with n cellscreate_sequence_a000108/1- A000108 - Catalan numbers: C(n), Also called Segner numbers.create_sequence_a000110/1- A000110 - Bell or exponential numbers: number of ways to partition a set of n labeled elementscreate_sequence_a000112/1- A000112 - Number of partially ordered sets ("posets") with n unlabeled elementscreate_sequence_a000123/1- A000123 - Number of binary partitions: number of partitions of 2n into powers of 2.create_sequence_a000161/1- A000161 - Number of partitions of n into 2 squares.create_sequence_a000166/1- A000166 - Subfactorial or rencontres numbers, or derangements ofncreate_sequence_a000169/1- A000169 - Number of labeled rooted trees with n nodes: n^(n-1)create_sequence_a000219/1- A000219 - Number of planar partitions (or plane partitions) of ncreate_sequence_a000262/1- A000262 - Number of "sets of lists"create_sequence_a000272/1- A000272 - Number of trees on n labeled nodescreate_sequence_a000312/1- A000312 - a(n) = n^n; number of labeled mappings from n points to themselvescreate_sequence_a000798/1- A000798 - Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elementscreate_sequence_a002033/1- A002033 - Number of perfect partitions of n.create_sequence_a002106/1- A002106 - Number of transitive permutation groups of degree ncreate_sequence_a002654/1- A002654 - Number of ways of writing n as a sum of at most two nonzero squares, where order matterscreate_sequence_a005470/1- A005470 - Number of unlabeled planar simple graphs with n nodescreate_sequence_a005588/1- A005588 - Number of free binary trees admitting height n.create_sequence_a006894/1- A006894 - Number of planted 3-trees of height < n.create_sequence_a006966/1- A006966 - Number of lattices on n unlabeled nodescreate_sequence_a055512/1- A055512 - Lattices with n labeled elementscreate_sequence_a001699/1- A001699 - Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative.create_sequence_a000311/1- A000311 - Schroeder's fourth problem; also series-reduced rooted trees with n labeled leaves; also number of total partitions of n.create_sequence_a001055/1- A001055 - The multiplicative partition function: number of ways of factoring n with all factors greater than 1create_sequence_a001190/1- A001190 - Wedderburn-Etherington numbers: unlabeled binary rooted treescreate_sequence_a003094/1- A003094 - Number of unlabeled connected planar simple graphs with n nodescreate_sequence_a000111/1- A000111 - Euler or up/down numberscreate_sequence_a000124/1- A000124 - Central polygonal numbers (the Lazy Caterer's sequence)create_sequence_a001045/1- A001045 - Jacobsthal sequence (or Jacobsthal numbers)create_sequence_a000670/1- A000670 - Fubini numbers
Constants
Core sequences of contant values or digits from expansions of non-integer constant values. See Chunky.Sequence.OEIS.Constants for non-core
sequences of constants.
create_sequence_a000004/1- A000004 - The zero sequencecreate_sequence_a000012/1- A000012 - The simplest sequence of positive numbers: the all 1's sequencecreate_sequence_a000796/1- A000796 - Decimal expansion of Picreate_sequence_a001333/1- A001333 - Numerators of continued fraction convergents to sqrt(2).
Primes
Core sequences about the primes, prime counting, or properties of primes. See Chunky.Sequence.OEIS.Primes for non-core sequences dealing
with prime numbers.
create_sequence_a000040/1- A000040 - The prime numbers.create_sequence_a000043/1- A000043 - Mersenne exponents: primes p such that 2^p - 1 is prime.create_sequence_a000720/1- A000720 - pi(n), the number of primes <= n.create_sequence_a001358/1- A001358 - Semiprimes (or biprimes): products of two primescreate_sequence_a002110/1- A002110 - Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.
Coefficients
Core sequences for coefficient calculations, like binomials.
create_sequence_a000521/1- A000521 - Coefficients of modular function j as power series in q = e^(2 Pi i t)create_sequence_a000984/1- A000984 - Central binomial coefficients: binomial(2*n,n)create_sequence_a001700/1- A001700 - a(n) = binomial(2n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1.create_sequence_a001764/1- A001764 - a(n) = binomial(3n,n)/(2n+1) (enumerates ternary trees and also noncrossing trees).create_sequence_a001405/1- A001405 - a(n) = binomial(n, floor(n/2)).
Triangles
Core sequences enumerating values in triangular numeric constructions, like Pascal's triangle.
create_sequence_a000217/1- A000217 - Triangular numbers: a(n) = binomial(n+1,2)create_sequence_a007318/1- A007318 - Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n.create_sequence_a008277/1- A008277 - Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.create_sequence_a008279/1- A008279 - Triangle T(n,k) = n!/(n-k)! (0 <= k <= n) read by rows, giving number of permutations of n things k at a time.create_sequence_a008292/1- A008292 - Triangle of Eulerian numbers T(n,k)create_sequence_a049310/1- A049310 - Triangle of coefficients of Chebyshev's S(n,x) := U(n,x/2) polynomials (exponents in increasing order).
Number Theory
Core sequences concerning general number theory, number sets, or ordered sets of values.
create_sequence_a000027/1- A000027 - The positive integerscreate_sequence_a000045/1- A000045 - Fibonacci Numberscreate_sequence_a000142/1- A000142 - Factorial numbers: n! = 1234...*ncreate_sequence_a001057/1- A001057 - Canonical enumeration of integers: interleaved positive and negative integers with zero prepended.create_sequence_a001147/1- A001147 - Double factorial of odd numbers: a(n) = (2n-1)!! = 135...(2n-1).create_sequence_a001477/1- A001477 - The nonnegative integers.create_sequence_a001478/1- A001478 - The negative integers.create_sequence_a001489/1- A001489 - a(n) = -n.create_sequence_a002808/1- A002808 - The composite numbers: numbers n of the form x*y for x > 1 and y > 1.create_sequence_a004526/1- A004526 - Nonnegative integers repeated, floor(n/2).create_sequence_a005843/1- A005843 - The nonnegative even numbers: a(n) = 2n.create_sequence_a005408/1- A005408 - The odd numbers: a(n) = 2*n + 1.create_sequence_a006882/1- A006882 - Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1.create_sequence_a018252/1- A018252 - The nonprime numbers: 1 together with the composite numbers, A002808.create_sequence_a000002/1- A000002 - Kolakoski sequencecreate_sequence_a000010/1- A000010 - Euler's totient functioncreate_sequence_a000032/1- A000032 - Lucas numbers beginning at 2create_sequence_a000109/1- A000109 - Number of simplicial polyhedra with n nodescreate_sequence_a000129/1- A000129 - Pell numbers: a(n) = 2*a(n-1) + a(n-2)create_sequence_a000204/1- A000204 - Lucas numbers (beginning with 1)create_sequence_a000292/1- A000292 - Tetrahedral (or triangular pyramidal) numberscreate_sequence_a000326/1- A000326 - Pentagonal numbers: a(n) = n(3n-1)/2.create_sequence_a000330/1- A000330 - Square pyramidal numberscreate_sequence_a000364/1- A000364 - Euler (or secant or "Zig") numberscreate_sequence_a000594/1- A000594 - Ramanujan's tau functioncreate_sequence_a000609/1- A000609 - Number of threshold functions of n or fewer variablescreate_sequence_a000688/1- A000688 - Number of Abelian groups of order ncreate_sequence_a000959/1- A000959 - Lucky numberscreate_sequence_a001003/1- A001003 - Schroeder's second problem; also called super-Catalan numbers or little Schroeder numberscreate_sequence_a001006/1- A001006 - Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n points on a circlecreate_sequence_a001519/1- A001519 - a(n) = 3*a(n-1) - a(n-2), with a(0) = a(1) = 1.create_sequence_a001615/1- A001615 - Dedekind psi functioncreate_sequence_a001906/1- A001906 - F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2).create_sequence_a002378/1- A002378 - Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).create_sequence_a002487/1- A002487 - Stern's diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2n) = a(n), a(2n+1) = a(n) + a(n+1).create_sequence_a002530/1- A002530 - a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1.create_sequence_a002531/1- A002531 - a(2n) = a(2n-1) + a(2n-2), a(2n+1) = 2a(2n) + a(2*n-1); a(0) = a(1) = 1.create_sequence_a003484/1- A003484 - Radon function, also called Hurwitz-Radon numberscreate_sequence_a006318/1- A006318 - Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers).create_sequence_a027642/1- A027642 - Denominator of Bernoulli number B_n.
Link to this section Summary
Functions
OEIS Sequence A000001 - Number of groups of order n.
OEIS Sequence A000002 - Kolakoski sequence
OEIS Sequence A000004 - The zero sequence.
OEIS Sequence A000005 - Number of divisors of N, simga-0(n), 𝝈0(n).
OEIS Sequence A000007 - The characteristic function of {0}: a(n) = 0^n.
OEIS Sequence A000009 - Number of partitions of n into distinct parts
OEIS Sequence A000010 - Euler's totient function phi(n)
OEIS Sequence A000012 - The simplest sequence of positive numbers: the all 1's sequence.
OEIS Sequence A000027 - The positive integers
OEIS Sequence A000029 - Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets).
OEIS Sequence A000031 - Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n.
OEIS Sequence A000032 - Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1.
OEIS Sequence A000035 - Period 2: repeat [0, 1]
OEIS Sequence A000040 - The prime numbers.
OEIS Sequence A000041 - Partitions of integer N
OEIS Sequence A000043 - Mersenne exponents: primes p such that 2^p - 1 is prime
OEIS Sequence A000045 - Fibonacci numbers
OEIS Sequence A000048 - Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged.
OEIS Sequence A000069 - Odious numbers: numbers with an odd number of 1's in their binary expansion.
OEIS Sequence A000079 - Powers of 2 a(n) = 2^n
OEIS Sequence A000081 - Number of unlabeled rooted trees with n nodes
OEIS Sequence A000085 - Number of self-inverse permutations on n letters, also known as involutions; number of standard Young tableaux with n cells.
OEIS Sequence A000105 - Number of free polyominoes (or square animals) with n cells.
OEIS Sequence A000108 - Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!). Also called Segner numbers.
OEIS Sequence A000109 - Number of simplicial polyhedra with n nodes
OEIS Sequence A000110 - Bell or exponential numbers: number of ways to partition a set of n labeled elements.
OEIS Sequence A000111 - Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also for n >= 2, half the number of alternating permutations on n letters (A001250).
OEIS Sequence A000112 - Number of partially ordered sets ("posets") with n unlabeled elements.
OEIS Sequence A000120 - 1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).
OEIS Sequence A000123 - Number of binary partitions: number of partitions of 2n into powers of 2.
OEIS Sequence A000124 - Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts.
OEIS Sequence A000129 - Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).
OEIS Sequence A000142 - Factorial numbers: n! = 1234...*n
OEIS Sequence A000161 - Number of partitions of n into 2 squares.
OEIS Sequence A000166 - Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.
OEIS Sequence A000169 - Number of labeled rooted trees with n nodes: n^(n-1).
OEIS Sequence A000203 - Sum of Divisors σ1(n)
OEIS Sequence A000204 - Lucas numbers (beginning with 1)
OEIS Sequence A000217 - Triangular numbers: a(n) = binomial(n+1,2)
OEIS Sequence A000219 - Number of planar partitions (or plane partitions) of n.
OEIS Sequence A000225 - a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)
OEIS Sequence A000244 - Powers of 3.
OEIS Sequence A000262 - Number of "sets of lists"
OEIS Sequence A000272 - Number of trees on n labeled nodes: n^(n-2) with a(0)=1.
OEIS Sequence A000290 - The squares: a(n) = n^2.
OEIS Sequence A000292 - Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n(n+1)(n+2)/6.
OEIS Sequence A000302 - Powers of 4: a(n) = 4^n.
OEIS Sequence A000311 - Schroeder's fourth problem; also series-reduced rooted trees with n labeled leaves; also number of total partitions of n.
OEIS Sequence A000312 - a(n) = n^n; number of labeled mappings from n points to themselves (endofunctions).
OEIS Sequence A000326 - Pentagonal numbers: a(n) = n(3n-1)/2.
OEIS Sequence A000330 - Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n(n+1)(2*n+1)/6.
OEIS Sequence A000364 - Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sec(x) = 1/cos(x).
OEIS Sequence A000396 - Perfect Numbers
OEIS Sequence A000521 - Coefficients of modular function j as power series in q = e^(2 Pi i t)
OEIS Sequence A000578 - The cubes: a(n) = n^3.
OEIS Sequence A000583 - Fourth powers: a(n) = n^4
OEIS Sequence A000593 - Sum of Odd Divisors of N
OEIS Sequence A000594 - Ramanujan's tau function
OEIS Sequence A000609 - Number of threshold functions of n or fewer variables.
OEIS Sequence A000670 - Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].
OEIS Sequence A000688 - Number of Abelian groups of order n
OEIS Sequence A000720 - pi(n), the number of primes <= n
OEIS Sequence A000796 - Decimal expansion of Pi (or digits of Pi).
OEIS Sequence A000798 - Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements.
OEIS Sequence A000959 - Lucky numbers.
OEIS Sequence A000961 - Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).
OEIS Sequence A000984 - Central binomial coefficients: binomial(2n,n) = (2n)!/(n!)^2.
OEIS Sequence A001003 - Schroeder's second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers.
OEIS Sequence A001006 - Motzkin numbers
OEIS Sequence A001045 - Jacobsthal sequence (or Jacobsthal numbers)
OEIS Sequence A001055 - The multiplicative partition function: number of ways of factoring n with all factors greater than 1 (a(1) = 1 by convention).
OEIS Sequence A001057 - Canonical enumeration of integers: interleaved positive and negative integers with zero prepended.
OEIS Sequence A001065 - Sum of proper divisors (Aliquot parts) of N.
OEIS Sequence A001147 - Double factorial of odd numbers: a(n) = (2n-1)!! = 135...(2n-1).
OEIS Sequence A001157 - Sum of squares of divisors of N, simga-2(n), 𝝈2(n).
OEIS Sequence A001190 - Wedderburn-Etherington numbers: unlabeled binary rooted trees (every node has out-degree 0 or 2) with n endpoints (and 2n-1 nodes in all).
OEIS Sequence A001221 - Number of distinct primes dividing n (also called omega(n)).
OEIS Sequence A001222 - Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n)).
OEIS Sequence A001227 - Number of odd divisors of n.
OEIS Sequence A001333 - Numerators of continued fraction convergents to sqrt(2).
OEIS Sequence A001358 - Semiprimes (or biprimes): products of two primes.
OEIS Sequence A001405 - a(n) = binomial(n, floor(n/2)).
OEIS Sequence A001477 - The nonnegative integers.
OEIS Sequence A001478 - The negative integers.
OEIS Sequence A001481 - Numbers that are the sum of 2 squares.
OEIS Sequence A001489 - a(n) = -n.
OEIS Sequence A001511 - The ruler function: 2^a(n) divides 2n
OEIS Sequence A001519 - a(n) = 3*a(n-1) - a(n-2), with a(0) = a(1) = 1.
OEIS Sequence A001615 - Dedekind psi function: n * Product_{p|n, p prime} (1 + 1/p).
OEIS Sequence A001699 - Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative.
OEIS Sequence A001700 - a(n) = binomial(2n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1.
OEIS Sequence A001764 - a(n) = binomial(3n,n)/(2n+1) (enumerates ternary trees and also noncrossing trees).
OEIS Sequence A001906 - F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2).
OEIS Sequence A001969 - Evil numbers: numbers with an even number of 1's in their binary expansion.
OEIS Sequence A002033 - Number of perfect partitions of n.
OEIS Sequence A002106 - Number of transitive permutation groups of degree n.
OEIS Sequence A002110 - Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.
OEIS Sequence A002113 - Palindromes in base 10.
OEIS Sequence A002275 - Repunits: (10^n - 1)/9. Often denoted by R_n.
OEIS Sequence A002378 - Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).
OEIS Sequence A002487 - Stern's diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2n) = a(n), a(2n+1) = a(n) + a(n+1).
OEIS Sequence A002530 - a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1.
OEIS Sequence A002531 - a(2n) = a(2n-1) + a(2n-2), a(2n+1) = 2a(2n) + a(2*n-1); a(0) = a(1) = 1.
OEIS Sequence A002620 - Quarter-squares: floor(n/2)*ceiling(n/2). Equivalently, floor(n^2/4).
OEIS Sequence A002654 - Number of ways of writing n as a sum of at most two nonzero squares, where order matters
OEIS Sequence A002808 - The composite numbers: numbers n of the form x*y for x > 1 and y > 1.
OEIS Sequence A003094 - Number of unlabeled connected planar simple graphs with n nodes.
OEIS Sequence A003418 - Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1.
OEIS Sequence A003484 - Radon function, also called Hurwitz-Radon numbers.
OEIS Sequence A004526 - Nonnegative integers repeated, floor(n/2).
OEIS Sequence A005100 - Deficient Numbers
OEIS Sequence A005101 - Abundant Numbers
OEIS Sequence A005117 - Squarefree numbers: numbers that are not divisible by a square greater than 1.
OEIS Sequence A005408 - The odd numbers: a(n) = 2*n + 1.
OEIS Sequence A005470 - Number of unlabeled planar simple graphs with n nodes.
OEIS Sequence A005588 - Number of free binary trees admitting height n.
OEIS Sequence A005811 - Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n.
OEIS Sequence A005843 - The nonnegative even numbers: a(n) = 2n.
OEIS Sequence A006318 - Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers).
OEIS Sequence A006530 - Gpf(n): greatest prime dividing n
OEIS Sequence A006882 - Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1.
OEIS Sequence A006894 - Number of planted 3-trees of height < n.
OEIS Sequence A006966 - Number of lattices on n unlabeled nodes.
OEIS Sequence A007318 - Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n.
OEIS Sequence A008277 - Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
OEIS Sequence A008279 - Triangle T(n,k) = n!/(n-k)! (0 <= k <= n) read by rows, giving number of permutations of n things k at a time.
OEIS Sequence A008292 - Triangle of Eulerian numbers T(n,k) (n >= 1, 1 <= k <= n) read by rows.
OEIS Sequence A008683 - Möbius (or Moebius) function mu(n)
OEIS Sequence A018252 - The nonprime numbers: 1 together with the composite numbers, A002808.
OEIS Sequence A020639 - Lpf(n): least prime dividing
OEIS Sequence A027642 - Denominator of Bernoulli number B_n.
OEIS Sequence A049310 - Triangle of coefficients of Chebyshev's S(n,x) := U(n,x/2) polynomials (exponents in increasing order).
OEIS Sequence A055512 - Lattices with n labeled elements.
OEIS Sequence A070939 - Length of binary representation of n.
OEIS Sequence A074206 - Kalmár's [Kalmar's] problem: number of ordered factorizations of n.
Link to this section Functions
OEIS Sequence A000001 - Number of groups of order n.
From OEIS A000001:
Number of groups of order n. (Formerly M0098 N0035)
Sequence IDs: :a000001
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000001) |> Sequence.take!(94)
[0,1,1,1,2,1,2,1,5,2,2,1,5,1,2,1,14,1,5,1,5,2,2,1,15,2,2,5,4,1,4,1,51,1,2,1,14,1,2,2,14,1,6,1,4,2,2,1,52,2,5,1,5,1,15,2,13,2,2,1,13,1,2,4,267,1,4,1,5,1,4,1,50,1,2,3,4,1,6,1,52,15,2,1,15,1,2,1,12,1,10,1,4,2]OEIS Sequence A000002 - Kolakoski sequence
From OEIS A000002:
Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's. (Formerly M0190 N0070)
Sequence IDs: :a000002
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000002) |> Sequence.take!(108)
[1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2,1,1,2,1,1,2,1,2,2,1,2,2,1,1,2,1,2,2,1,2,1,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,1,2,2,1,2,1,1,2,2,1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,2,2,1,2,1,1,2,1,2,2]OEIS Sequence A000004 - The zero sequence.
From OEIS A000004:
The zero sequence. (Formerly M0000)
Sequence IDs: :a000004
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000004) |> Sequence.take!(102)
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]OEIS Sequence A000005 - Number of divisors of N, simga-0(n), 𝝈0(n).
From OEIS A000005:
d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n. (Formerly M0246 N0086)
Sequence IDs: :a000005
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000005) |> Sequence.take!(10)
[1, 2, 2, 3, 2, 4, 2, 4, 3, 4]OEIS Sequence A000007 - The characteristic function of {0}: a(n) = 0^n.
From OEIS A000007:
The characteristic function of {0}: a(n) = 0^n. (Formerly M0002)
Sequence IDs: :a000007
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000007) |> Sequence.take!(105)
[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]OEIS Sequence A000009 - Number of partitions of n into distinct parts
From OEIS A000009:
Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts (if n > 0). (Formerly M0281 N0100)
Divergence
Calculation of this sequence is based on translation of a Maxima program by Vladimir Kruchinin,
and diverges from canonical results for n > 10.
Sequence IDs: :a000009
Finite: False
Offset: 0
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000009) |> Sequence.take!(10)
[1, 1, 1, 2, 2, 3, 4, 5, 6, 8]OEIS Sequence A000010 - Euler's totient function phi(n)
From OEIS A000010:
Euler totient function phi(n): count numbers <= n and prime to n. (Formerly M0299 N0111)
Sequence IDs: :a000010
Finite: false
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000010) |> Sequence.take!(20)
[1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8]OEIS Sequence A000012 - The simplest sequence of positive numbers: the all 1's sequence.
From OEIS A000012:
The simplest sequence of positive numbers: the all 1's sequence. (Formerly M0003)
Sequence IDs: :a000012
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000012) |> Sequence.take!(90)
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]OEIS Sequence A000027 - The positive integers
From OEIS A000027:
The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous. (Formerly M0472 N0173)
Sequence IDs: :a000027
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000027) |> Sequence.take!(77)
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77]OEIS Sequence A000029 - Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets).
From OEIS A000029:
Number of necklaces with n beads of 2 colors, allowing turning over (these are also called bracelets). (Formerly M0563 N0202)
Sequence IDs: :a000029
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000029) |> Sequence.take!(36)
[1,2,3,4,6,8,13,18,30,46,78,126,224,380,687,1224,2250,4112,7685,14310,27012,50964,96909,184410,352698,675188,1296858,2493726,4806078,9272780,17920860,34669602,67159050,130216124,252745368,490984488]OEIS Sequence A000031 - Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n.
From OEIS A000031:
Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n. (Formerly M0564 N0203)
Sequence IDs: :a000031
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000031) |> Sequence.take!(36)
[1,2,3,4,6,8,14,20,36,60,108,188,352,632,1182,2192,4116,7712,14602,27596,52488,99880,190746,364724,699252,1342184,2581428,4971068,9587580,18512792,35792568,69273668,134219796,260301176,505294128,981706832]OEIS Sequence A000032 - Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1.
From OEIS A000032:
Lucas numbers beginning at 2: L(n) = L(n-1) + L(n-2), L(0) = 2, L(1) = 1. (Formerly M0155)
Sequence IDs: :a000032
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000032) |> Sequence.take!(39)
[2,1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127,24476,39603,64079,103682,167761,271443,439204,710647,1149851,1860498,3010349,4870847,7881196,12752043,20633239,33385282,54018521,87403803]OEIS Sequence A000035 - Period 2: repeat [0, 1]
From OEIS A000035:
Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n. (Formerly M0001)
Sequence IDs: :a000035
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000035) |> Sequence.take!(105)
[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]OEIS Sequence A000040 - The prime numbers.
From OEIS A000040:
The prime numbers. (Formerly M0652 N0241)
Sequence IDs: :a000040
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000040) |> Sequence.take!(58)
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271]OEIS Sequence A000041 - Partitions of integer N
This sequence contains the partitions of the integers from 0 to 250.
From Wikipedia:
In number theory, the partition function
p(n)represents the number of possible partitions of a non-negative integern. For instance,p(4) = 5because the integer4has the five partitions:1 + 1 + 1 + 1,1 + 1 + 2,1 + 3,2 + 2, and4.
From OEIS A000041:
a(n) is the number of partitions of n (the partition numbers). (Formerly M0663 N0244)
Sequence IDs: :a000041
Finite: true
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000041) |> Sequence.take!(10)
[1, 1, 2, 3, 5, 7, 11, 15, 22, 30]OEIS Sequence A000043 - Mersenne exponents: primes p such that 2^p - 1 is prime
From OEIS A000043:
Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime. (Formerly M0672 N0248)
Sequence IDs: :a000043
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000043) |> Sequence.take!(47)
[2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,216091,756839,859433,1257787,1398269,2976221,3021377,6972593,13466917,20996011,24036583,25964951,30402457,32582657,37156667,42643801,43112609]OEIS Sequence A000045 - Fibonacci numbers
From OEIS A000045
Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1. (Formerly M0692 N0256)
Sequence IDs: :a000045, :fibonacci
Finite: false
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000045) |> Sequence.take!(10)
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]OEIS Sequence A000048 - Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged.
From OEIS A000048:
Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged. (Formerly M0711 N0262)
Sequence IDs: :a000048
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000048) |> Sequence.take!(38)
[1,1,1,1,2,3,5,9,16,28,51,93,170,315,585,1091,2048,3855,7280,13797,26214,49929,95325,182361,349520,671088,1290555,2485504,4793490,9256395,17895679,34636833,67108864,130150493,252645135,490853403,954437120,1857283155]OEIS Sequence A000069 - Odious numbers: numbers with an odd number of 1's in their binary expansion.
From OEIS A000069:
Odious numbers: numbers with an odd number of 1's in their binary expansion. (Formerly M1031 N0388)
Sequence IDs: :a000069
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000069) |> Sequence.take!(65)
[1,2,4,7,8,11,13,14,16,19,21,22,25,26,28,31,32,35,37,38,41,42,44,47,49,50,52,55,56,59,61,62,64,67,69,70,73,74,76,79,81,82,84,87,88,91,93,94,97,98,100,103,104,107,109,110,112,115,117,118,121,122,124,127,128]OEIS Sequence A000079 - Powers of 2 a(n) = 2^n
From OEIS A000009:
Powers of 2: a(n) = 2^n. (Formerly M1129 N0432)
Sequence IDs: :a000079
Finite: False
Offset: 0
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000079) |> Sequence.take!(20)
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288]OEIS Sequence A000081 - Number of unlabeled rooted trees with n nodes
From OEIS A000081:
Number of unlabeled rooted trees with n nodes (or connected functions with a fixed point). (Formerly M1180 N0454)
Sequence IDs: :a000081
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000081) |> Sequence.take!(31)
[0,1,1,2,4,9,20,48,115,286,719,1842,4766,12486,32973,87811,235381,634847,1721159,4688676,12826228,35221832,97055181,268282855,743724984,2067174645,5759636510,16083734329,45007066269,126186554308,354426847597]OEIS Sequence A000085 - Number of self-inverse permutations on n letters, also known as involutions; number of standard Young tableaux with n cells.
From OEIS A000085:
Number of self-inverse permutations on n letters, also known as involutions; number of standard Young tableaux with n cells. (Formerly M1221 N0469)
Sequence IDs: :a000085
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000085) |> Sequence.take!(28)
[1,1,2,4,10,26,76,232,764,2620,9496,35696,140152,568504,2390480,10349536,46206736,211799312,997313824,4809701440,23758664096,119952692896,618884638912,3257843882624,17492190577600,95680443760576,532985208200576,3020676745975552]OEIS Sequence A000105 - Number of free polyominoes (or square animals) with n cells.
From OEIS A000105:
Number of free polyominoes (or square animals) with n cells. (Formerly M1425 N0561)
Sequence IDs: :a000105
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000105) |> Sequence.take!(29)
[1,1,1,2,5,12,35,108,369,1285,4655,17073,63600,238591,901971,3426576,13079255,50107909,192622052,742624232,2870671950,11123060678,43191857688,168047007728,654999700403,2557227044764,9999088822075,39153010938487,153511100594603]OEIS Sequence A000108 - Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!). Also called Segner numbers.
From OEIS A000108:
Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!). Also called Segner numbers. (Formerly M1459 N0577)
Sequence IDs: :a000108
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000108) |> Sequence.take!(31)
[1,1,2,5,14,42,132,429,1430,4862,16796,58786,208012,742900,2674440,9694845,35357670,129644790,477638700,1767263190,6564120420,24466267020,91482563640,343059613650,1289904147324,4861946401452,18367353072152,69533550916004,263747951750360,1002242216651368,3814986502092304]OEIS Sequence A000109 - Number of simplicial polyhedra with n nodes
From OEIS A000109:
Number of simplicial polyhedra with n nodes; simple planar graphs with 3n-6 edges; maximal simple planar graphs; 3-connected planar triangulations; 3-connected triangulations of the sphere; 3-connected cubic planar graphs. (Formerly M1469 N0580)
Sequence IDs: :a000109
Finite: False
Offset: 3
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000109) |> Sequence.take!(21)
[1,1,1,2,5,14,50,233,1249,7595,49566,339722,2406841,17490241,129664753,977526957,7475907149,57896349553,453382272049,3585853662949,28615703421545]OEIS Sequence A000110 - Bell or exponential numbers: number of ways to partition a set of n labeled elements.
From OEIS A000110:
Bell or exponential numbers: number of ways to partition a set of n labeled elements. (Formerly M1484 N0585)
Sequence IDs: :a000110
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000110) |> Sequence.take!(27)
[1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,190899322,1382958545,10480142147,82864869804,682076806159,5832742205057,51724158235372,474869816156751,4506715738447323,44152005855084346,445958869294805289,4638590332229999353,49631246523618756274]OEIS Sequence A000111 - Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also for n >= 2, half the number of alternating permutations on n letters (A001250).
From OEIS A000111:
Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also for n >= 2, half the number of alternating permutations on n letters (A001250). (Formerly M1492 N0587)
Sequence IDs: :a000111
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000111) |> Sequence.take!(27)
[1,1,1,2,5,16,61,272,1385,7936,50521,353792,2702765,22368256,199360981,1903757312,19391512145,209865342976,2404879675441,29088885112832,370371188237525,4951498053124096,69348874393137901,1015423886506852352,15514534163557086905,246921480190207983616,4087072509293123892361]OEIS Sequence A000112 - Number of partially ordered sets ("posets") with n unlabeled elements.
From OEIS A000112:
Number of partially ordered sets ("posets") with n unlabeled elements. (Formerly M1495 N0588)
Sequence IDs: :a000112
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000112) |> Sequence.take!(17)
[1,1,2,5,16,63,318,2045,16999,183231,2567284,46749427,1104891746,33823827452,1338193159771,68275077901156,4483130665195087]OEIS Sequence A000120 - 1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).
From OEIS A000120:
1's-counting sequence: number of 1's in binary expansion of n (or the binary weight of n). (Formerly M0105 N0041)
Sequence IDs: :a000120
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000120) |> Sequence.take!(105)
[0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,3]OEIS Sequence A000123 - Number of binary partitions: number of partitions of 2n into powers of 2.
From OEIS A000123:
Number of binary partitions: number of partitions of 2n into powers of 2. (Formerly M1011 N0378)
Sequence IDs: :a000123
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000123) |> Sequence.take!(51)
[1,2,4,6,10,14,20,26,36,46,60,74,94,114,140,166,202,238,284,330,390,450,524,598,692,786,900,1014,1154,1294,1460,1626,1828,2030,2268,2506,2790,3074,3404,3734,4124,4514,4964,5414,5938,6462,7060,7658,8350,9042,9828]OEIS Sequence A000124 - Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts.
From OEIS A000124:
Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts. (Formerly M1041 N0391)
Sequence IDs: :a000124
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000124) |> Sequence.take!(53)
[1,2,4,7,11,16,22,29,37,46,56,67,79,92,106,121,137,154,172,191,211,232,254,277,301,326,352,379,407,436,466,497,529,562,596,631,667,704,742,781,821,862,904,947,991,1036,1082,1129,1177,1226,1276,1327,1379]OEIS Sequence A000129 - Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).
From OEIS A000129:
Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2). (Formerly M1413 N0552)
Sequence IDs: :a000129
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000129) |> Sequence.take!(32)
[0,1,2,5,12,29,70,169,408,985,2378,5741,13860,33461,80782,195025,470832,1136689,2744210,6625109,15994428,38613965,93222358,225058681,543339720,1311738121,3166815962,7645370045,18457556052,44560482149,107578520350,259717522849]OEIS Sequence A000142 - Factorial numbers: n! = 1234...*n
From OEIS A000142:
Factorial numbers: n! = 1234...*n (order of symmetric group S_n, number of permutations of n letters). (Formerly M1675 N0659)
Sequence IDs: :a000142
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000142) |> Sequence.take!(23)
[1,1,2,6,24,120,720,5040,40320,362880,3628800,39916800,479001600,6227020800,87178291200,1307674368000,20922789888000,355687428096000,6402373705728000,121645100408832000,2432902008176640000,51090942171709440000,1124000727777607680000]OEIS Sequence A000161 - Number of partitions of n into 2 squares.
From OEIS A000161:
Number of partitions of n into 2 squares.
Sequence IDs: :a000161
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000161) |> Sequence.take!(108)
[1,1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0,0,2,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,0,0,1,2,0,1,1,0,0,0,0,1,0,0,1,0,0,1,2,0,0,1,0,0,0,1,1,1,0,0,0,0,0,1,1,1,0,0,2,0,0,0,1,1,0,0,0,0,0,0,1,1,0,2,1,0,0,1,0,1,0]OEIS Sequence A000166 - Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points.
From OEIS A000166:
Subfactorial or rencontres numbers, or derangements: number of permutations of n elements with no fixed points. (Formerly M1937 N0766)
Sequence IDs: :a000166
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000166) |> Sequence.take!(24)
[1,0,1,2,9,44,265,1854,14833,133496,1334961,14684570,176214841,2290792932,32071101049,481066515734,7697064251745,130850092279664,2355301661033953,44750731559645106,895014631192902121,18795307255050944540,413496759611120779881,9510425471055777937262]OEIS Sequence A000169 - Number of labeled rooted trees with n nodes: n^(n-1).
From OEIS A000169:
Number of labeled rooted trees with n nodes: n^(n-1). (Formerly M1946 N0771)
Sequence IDs: :a000169
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000169) |> Sequence.take!(20)
[1,2,9,64,625,7776,117649,2097152,43046721,1000000000,25937424601,743008370688,23298085122481,793714773254144,29192926025390625,1152921504606846976,48661191875666868481,2185911559738696531968,104127350297911241532841,5242880000000000000000000]OEIS Sequence A000203 - Sum of Divisors σ1(n)
From OEIS A000203:
(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n). (Formerly M2329 N0921)
Sequence IDs: :a000203
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000203) |> Sequence.take!(20)
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42] OEIS Sequence A000204 - Lucas numbers (beginning with 1)
From OEIS A000204:
Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3. (Formerly M2341 N0924)
Sequence IDs: :a000204
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000204) |> Sequence.take!(39)
[1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127,24476,39603,64079,103682,167761,271443,439204,710647,1149851,1860498,3010349,4870847,7881196,12752043,20633239,33385282,54018521,87403803,141422324]OEIS Sequence A000217 - Triangular numbers: a(n) = binomial(n+1,2)
From OEIS A000217:
Triangular numbers: a(n) = binomial(n+1,2) = n(n+1)/2 = 0 + 1 + 2 + ... + n. (Formerly M2535 N1002)
Sequence IDs: :a000217
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000217) |> Sequence.take!(54)
[0,1,3,6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231,253,276,300,325,351,378,406,435,465,496,528,561,595,630,666,703,741,780,820,861,903,946,990,1035,1081,1128,1176,1225,1275,1326,1378,1431]OEIS Sequence A000219 - Number of planar partitions (or plane partitions) of n.
From OEIS A000219:
Number of planar partitions (or plane partitions) of n. (Formerly M2566 N1016)
Sequence IDs: :a000219
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000219) |> Sequence.take!(41)
[1,1,3,6,13,24,48,86,160,282,500,859,1479,2485,4167,6879,11297,18334,29601,47330,75278,118794,186475,290783,451194,696033,1068745,1632658,2483234,3759612,5668963,8512309,12733429,18974973,28175955,41691046,61484961,90379784,132441995,193487501,281846923]OEIS Sequence A000225 - a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)
From OEIS A000225:
a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.) (Formerly M2655 N1059)
Sequence IDs: :a000225
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000225) |> Sequence.take!(33)
[0,1,3,7,15,31,63,127,255,511,1023,2047,4095,8191,16383,32767,65535,131071,262143,524287,1048575,2097151,4194303,8388607,16777215,33554431,67108863,134217727,268435455,536870911,1073741823,2147483647,4294967295]OEIS Sequence A000244 - Powers of 3.
From OEIS A000244:
Powers of 3. (Formerly M2807 N1129)
Sequence IDs: :a000244
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000244) |> Sequence.take!(28)
[1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,4782969,14348907,43046721,129140163,387420489,1162261467,3486784401,10460353203,31381059609,94143178827,282429536481,847288609443,2541865828329,7625597484987]OEIS Sequence A000262 - Number of "sets of lists"
From OEIS A000262:
Number of "sets of lists": number of partitions of {1,...,n} into any number of lists, where a list means an ordered subset. (Formerly M2950 N1190)
Sequence IDs: :a000262
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000262) |> Sequence.take!(22)
[1,1,3,13,73,501,4051,37633,394353,4596553,58941091,824073141,12470162233,202976401213,3535017524403,65573803186921,1290434218669921,26846616451246353,588633468315403843,13564373693588558173,327697927886085654441,8281153039765859726341]OEIS Sequence A000272 - Number of trees on n labeled nodes: n^(n-2) with a(0)=1.
From OEIS A000272:
Number of trees on n labeled nodes: n^(n-2) with a(0)=1. (Formerly M3027 N1227)
Sequence IDs: :a000272
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000272) |> Sequence.take!(20)
[1,1,1,3,16,125,1296,16807,262144,4782969,100000000,2357947691,61917364224,1792160394037,56693912375296,1946195068359375,72057594037927936,2862423051509815793,121439531096594251776,5480386857784802185939]OEIS Sequence A000290 - The squares: a(n) = n^2.
From OEIS A000290:
The squares: a(n) = n^2. (Formerly M3356 N1350)
Sequence IDs: :a000290
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000290) |> Sequence.take!(51)
[0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961,1024,1089,1156,1225,1296,1369,1444,1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,2401,2500]OEIS Sequence A000292 - Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n(n+1)(n+2)/6.
From OEIS A000292:
Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n(n+1)(n+2)/6. (Formerly M3382 N1363)
Sequence IDs: :a000292
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000292) |> Sequence.take!(45)
[0,1,4,10,20,35,56,84,120,165,220,286,364,455,560,680,816,969,1140,1330,1540,1771,2024,2300,2600,2925,3276,3654,4060,4495,4960,5456,5984,6545,7140,7770,8436,9139,9880,10660,11480,12341,13244,14190,15180]OEIS Sequence A000302 - Powers of 4: a(n) = 4^n.
From OEIS A000302:
Powers of 4: a(n) = 4^n. (Formerly M3518 N1428)
Sequence IDs: :a000302
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000302) |> Sequence.take!(25)
[1,4,16,64,256,1024,4096,16384,65536,262144,1048576,4194304,16777216,67108864,268435456,1073741824,4294967296,17179869184,68719476736,274877906944,1099511627776,4398046511104,17592186044416,70368744177664,281474976710656]OEIS Sequence A000311 - Schroeder's fourth problem; also series-reduced rooted trees with n labeled leaves; also number of total partitions of n.
From OEIS A000311:
Schroeder's fourth problem; also series-reduced rooted trees with n labeled leaves; also number of total partitions of n. (Formerly M3613 N1465)
Sequence IDs: :a000311
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000311) |> Sequence.take!(20)
[0,1,1,4,26,236,2752,39208,660032,12818912,282137824,6939897856,188666182784,5617349020544,181790703209728,6353726042486272,238513970965257728,9571020586419012608,408837905660444010496,18522305410364986906624]OEIS Sequence A000312 - a(n) = n^n; number of labeled mappings from n points to themselves (endofunctions).
From OEIS A000312:
a(n) = n^n; number of labeled mappings from n points to themselves (endofunctions). (Formerly M3619 N1469)
Sequence IDs: :a000312
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000312) |> Sequence.take!(18)
[1,1,4,27,256,3125,46656,823543,16777216,387420489,10000000000,285311670611,8916100448256,302875106592253,11112006825558016,437893890380859375,18446744073709551616,827240261886336764177]OEIS Sequence A000326 - Pentagonal numbers: a(n) = n(3n-1)/2.
From OEIS A000326:
Pentagonal numbers: a(n) = n(3n-1)/2. (Formerly M3818 N1562)
Sequence IDs: :a000326
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000326) |> Sequence.take!(47)
[0,1,5,12,22,35,51,70,92,117,145,176,210,247,287,330,376,425,477,532,590,651,715,782,852,925,1001,1080,1162,1247,1335,1426,1520,1617,1717,1820,1926,2035,2147,2262,2380,2501,2625,2752,2882,3015,3151]OEIS Sequence A000330 - Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n(n+1)(2*n+1)/6.
From OEIS A000330:
Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n(n+1)(2*n+1)/6. (Formerly M3844 N1574)
Sequence IDs: :a000330
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000330) |> Sequence.take!(45)
[0,1,5,14,30,55,91,140,204,285,385,506,650,819,1015,1240,1496,1785,2109,2470,2870,3311,3795,4324,4900,5525,6201,6930,7714,8555,9455,10416,11440,12529,13685,14910,16206,17575,19019,20540,22140,23821,25585,27434,29370]OEIS Sequence A000364 - Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sec(x) = 1/cos(x).
From OEIS A000364:
Euler (or secant or "Zig") numbers: e.g.f. (even powers only) sec(x) = 1/cos(x). (Formerly M4019 N1667)
Sequence IDs: :a000364
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000364) |> Sequence.take!(17)
[1,1,5,61,1385,50521,2702765,199360981,19391512145,2404879675441,370371188237525,69348874393137901,15514534163557086905,4087072509293123892361,1252259641403629865468285,441543893249023104553682821,177519391579539289436664789665]OEIS Sequence A000396 - Perfect Numbers
From OEIS A000396:
Perfect numbers n: n is equal to the sum of the proper divisors of n. (Formerly M4186 N1744)
Sequence IDs: :a000396
Finite: True
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000396) |> Sequence.take!(5)
[6, 28, 496, 8128, 33550336] OEIS Sequence A000521 - Coefficients of modular function j as power series in q = e^(2 Pi i t)
From OEIS A000521:
Coefficients of modular function j as power series in q = e^(2 Pi i t). Another name is the elliptic modular invariant J(tau). (Formerly M5477 N2372)
Sequence IDs: :a000521
Finite: False
Offset: -1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000521) |> Sequence.take!(17)
[1,744,196884,21493760,864299970,20245856256,333202640600,4252023300096,44656994071935,401490886656000,3176440229784420,22567393309593600,146211911499519294,874313719685775360,4872010111798142520,25497827389410525184,126142916465781843075]OEIS Sequence A000578 - The cubes: a(n) = n^3.
From OEIS A000578:
The cubes: a(n) = n^3. (Formerly M4499 N1905)
Sequence IDs: :a000578
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000578) |> Sequence.take!(41)
[0,1,8,27,64,125,216,343,512,729,1000,1331,1728,2197,2744,3375,4096,4913,5832,6859,8000,9261,10648,12167,13824,15625,17576,19683,21952,24389,27000,29791,32768,35937,39304,42875,46656,50653,54872,59319,64000]OEIS Sequence A000583 - Fourth powers: a(n) = n^4
From OEIS A000583:
Fourth powers: a(n) = n^4. (Formerly M5004 N2154)
Sequence IDs: :a000583
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000583) |> Sequence.take!(34)
[0,1,16,81,256,625,1296,2401,4096,6561,10000,14641,20736,28561,38416,50625,65536,83521,104976,130321,160000,194481,234256,279841,331776,390625,456976,531441,614656,707281,810000,923521,1048576,1185921]OEIS Sequence A000593 - Sum of Odd Divisors of N
From OEIS A000593:
Sum of odd divisors of n. (Formerly M3197 N1292)
Sequence IDs: :a000593
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000593) |> Sequence.take!(10)
[1, 1, 4, 1, 6, 4, 8, 1, 13, 6]OEIS Sequence A000594 - Ramanujan's tau function
From OEIS A000594:
Ramanujan's tau function (or Ramanujan numbers, or tau numbers). (Formerly M5153 N2237)
Sequence IDs: :a000594
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000594) |> Sequence.take!(28)
[1,-24,252,-1472,4830,-6048,-16744,84480,-113643,-115920,534612,-370944,-577738,401856,1217160,987136,-6905934,2727432,10661420,-7109760,-4219488,-12830688,18643272,21288960,-25499225,13865712,-73279080,24647168]OEIS Sequence A000609 - Number of threshold functions of n or fewer variables.
From OEIS A000609:
Number of threshold functions of n or fewer variables. (Formerly M1285 N0492)
Sequence IDs: :a000609
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000609) |> Sequence.take!(10)
[2,4,14,104,1882,94572,15028134,8378070864,17561539552946,144130531453121108]OEIS Sequence A000670 - Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n].
From OEIS A000670:
Fubini numbers: number of preferential arrangements of n labeled elements; or number of weak orders on n labeled elements; or number of ordered partitions of [n]. (Formerly M2952 N1191)
Sequence IDs: :a000670
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000670) |> Sequence.take!(21)
[1,1,3,13,75,541,4683,47293,545835,7087261,102247563,1622632573,28091567595,526858348381,10641342970443,230283190977853,5315654681981355,130370767029135901,3385534663256845323,92801587319328411133,2677687796244384203115]OEIS Sequence A000688 - Number of Abelian groups of order n
From OEIS A000688:
Number of Abelian groups of order n; number of factorizations of n into prime powers. (Formerly M0064 N0020)
Sequence IDs: :a000688
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000688) |> Sequence.take!(107)
[1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,5,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,7,1,1,1,4,1,1,1,3,1,1,1,2,2,1,1,5,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,11,1,1,1,2,1,1,1,6,1,1,2,2,1,1,1,5,5,1,1,2,1,1,1,3,1,2,1,2,1,1,1,7,1,2,2,4,1,1,1,3,1,1,1]OEIS Sequence A000720 - pi(n), the number of primes <= n
From OEIS A000720:
pi(n), the number of primes <= n. Sometimes called PrimePi(n) to distinguish it from the number 3.14159... (Formerly M0256 N0090)
Sequence IDs: :a000720
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000720) |> Sequence.take!(78)
[0,1,2,2,3,3,4,4,4,4,5,5,6,6,6,6,7,7,8,8,8,8,9,9,9,9,9,9,10,10,11,11,11,11,11,11,12,12,12,12,13,13,14,14,14,14,15,15,15,15,15,15,16,16,16,16,16,16,17,17,18,18,18,18,18,18,19,19,19,19,20,20,21,21,21,21,21,21]OEIS Sequence A000796 - Decimal expansion of Pi (or digits of Pi).
From OEIS A000796:
Decimal expansion of Pi (or digits of Pi). (Formerly M2218 N0880)
Sequence IDs: :a000796
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000796) |> Sequence.take!(105)
[3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5,0,2,8,8,4,1,9,7,1,6,9,3,9,9,3,7,5,1,0,5,8,2,0,9,7,4,9,4,4,5,9,2,3,0,7,8,1,6,4,0,6,2,8,6,2,0,8,9,9,8,6,2,8,0,3,4,8,2,5,3,4,2,1,1,7,0,6,7,9,8,2,1,4]OEIS Sequence A000798 - Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements.
From OEIS A000798:
Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements. (Formerly M3631 N1476)
Sequence IDs: :a000798
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000798) |> Sequence.take!(19)
[1,1,4,29,355,6942,209527,9535241,642779354,63260289423,8977053873043,1816846038736192,519355571065774021,207881393656668953041,115617051977054267807460,88736269118586244492485121,93411113411710039565210494095,134137950093337880672321868725846,261492535743634374805066126901117203]OEIS Sequence A000959 - Lucky numbers.
From OEIS A000959:
Lucky numbers. (Formerly M2616 N1035)
Sequence IDs: :a000959
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000959) |> Sequence.take!(57)
[1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79,87,93,99,105,111,115,127,129,133,135,141,151,159,163,169,171,189,193,195,201,205,211,219,223,231,235,237,241,259,261,267,273,283,285,289,297,303]OEIS Sequence A000961 - Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).
From OEIS A000961:
Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1). (Formerly M0517 N0185)
Sequence IDs: :a000961
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000961) |> Sequence.take!(64)
[1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,47,49,53,59,61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,125,127,128,131,137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,211,223,227]OEIS Sequence A000984 - Central binomial coefficients: binomial(2n,n) = (2n)!/(n!)^2.
From OEIS A000984:
Central binomial coefficients: binomial(2n,n) = (2n)!/(n!)^2. (Formerly M1645 N0643)
Sequence IDs: :a000984
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a000984) |> Sequence.take!(28)
[1,2,6,20,70,252,924,3432,12870,48620,184756,705432,2704156,10400600,40116600,155117520,601080390,2333606220,9075135300,35345263800,137846528820,538257874440,2104098963720,8233430727600,32247603683100,126410606437752,495918532948104,1946939425648112]OEIS Sequence A001003 - Schroeder's second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers.
From OEIS A001003:
Schroeder's second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers. (Formerly M2898 N1163)
Sequence IDs: :a001003
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001003) |> Sequence.take!(24)
[1,1,3,11,45,197,903,4279,20793,103049,518859,2646723,13648869,71039373,372693519,1968801519,10463578353,55909013009,300159426963,1618362158587,8759309660445,47574827600981,259215937709463,1416461675464871]OEIS Sequence A001006 - Motzkin numbers
From OEIS A001006:
Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle. (Formerly M1184 N0456)
Sequence IDs: :a001006
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001006) |> Sequence.take!(30)
[1,1,2,4,9,21,51,127,323,835,2188,5798,15511,41835,113634,310572,853467,2356779,6536382,18199284,50852019,142547559,400763223,1129760415,3192727797,9043402501,25669818476,73007772802,208023278209,593742784829]OEIS Sequence A001045 - Jacobsthal sequence (or Jacobsthal numbers)
From OEIS A001045:
Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1. (Formerly M2482 N0983)
Sequence IDs: :a001045
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001045) |> Sequence.take!(35)
[0,1,1,3,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,174763,349525,699051,1398101,2796203,5592405,11184811,22369621,44739243,89478485,178956971,357913941,715827883,1431655765,2863311531,5726623061]OEIS Sequence A001055 - The multiplicative partition function: number of ways of factoring n with all factors greater than 1 (a(1) = 1 by convention).
From OEIS A001055:
The multiplicative partition function: number of ways of factoring n with all factors greater than 1 (a(1) = 1 by convention). (Formerly M0095 N0032)
Sequence IDs: :a001055
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001055) |> Sequence.take!(103)
[1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,5,1,4,1,4,2,2,1,7,2,2,3,4,1,5,1,7,2,2,2,9,1,2,2,7,1,5,1,4,4,2,1,12,2,4,2,4,1,7,2,7,2,2,1,11,1,2,4,11,2,5,1,4,2,5,1,16,1,2,4,4,2,5,1,12,5,2,1,11,2,2,2,7,1,11,2,4,2,2,2,19,1,4,4,9,1,5,1]OEIS Sequence A001057 - Canonical enumeration of integers: interleaved positive and negative integers with zero prepended.
From OEIS A001057:
Canonical enumeration of integers: interleaved positive and negative integers with zero prepended.
Sequence IDs: :a001057
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001057) |> Sequence.take!(63)
[0,1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,8,-8,9,-9,10,-10,11,-11,12,-12,13,-13,14,-14,15,-15,16,-16,17,-17,18,-18,19,-19,20,-20,21,-21,22,-22,23,-23,24,-24,25,-25,26,-26,27,-27,28,-28,29,-29,30,-30,31,-31]OEIS Sequence A001065 - Sum of proper divisors (Aliquot parts) of N.
From OEIS A001065:
Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n. (Formerly M2226 N0884)
Sequence IDs: :a001065
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a001065) |> Sequence.take!(20)
[0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22]OEIS Sequence A001147 - Double factorial of odd numbers: a(n) = (2n-1)!! = 135...(2n-1).
From OEIS A001147:
Double factorial of odd numbers: a(n) = (2n-1)!! = 135...(2n-1). (Formerly M3002 N1217)
Sequence IDs: :a001147
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001147) |> Sequence.take!(20)
[1,1,3,15,105,945,10395,135135,2027025,34459425,654729075,13749310575,316234143225,7905853580625,213458046676875,6190283353629375,191898783962510625,6332659870762850625,221643095476699771875,8200794532637891559375]OEIS Sequence A001157 - Sum of squares of divisors of N, simga-2(n), 𝝈2(n).
From OEIS A001157:
sigma_2(n): sum of squares of divisors of n. (Formerly M3799 N1551)
Sequence IDs: :a001157
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a001157) |> Sequence.take!(10)
[1, 5, 10, 21, 26, 50, 50, 85, 91, 130]OEIS Sequence A001190 - Wedderburn-Etherington numbers: unlabeled binary rooted trees (every node has out-degree 0 or 2) with n endpoints (and 2n-1 nodes in all).
From OEIS A001190:
Wedderburn-Etherington numbers: unlabeled binary rooted trees (every node has out-degree 0 or 2) with n endpoints (and 2n-1 nodes in all). (Formerly M0790 N0298)
Sequence IDs: :a001190
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001190) |> Sequence.take!(35)
[0,1,1,1,2,3,6,11,23,46,98,207,451,983,2179,4850,10905,24631,56011,127912,293547,676157,1563372,3626149,8436379,19680277,46026618,107890609,253450711,596572387,1406818759,3323236238,7862958391,18632325319,44214569100]OEIS Sequence A001221 - Number of distinct primes dividing n (also called omega(n)).
From OEIS A001221:
Number of distinct primes dividing n (also called omega(n)). (Formerly M0056 N0019)
Sequence IDs: :a001221
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001221) |> Sequence.take!(111)
[0,1,1,1,1,2,1,1,1,2,1,2,1,2,2,1,1,2,1,2,2,2,1,2,1,2,1,2,1,3,1,1,2,2,2,2,1,2,2,2,1,3,1,2,2,2,1,2,1,2,2,2,1,2,2,2,2,2,1,3,1,2,2,1,2,3,1,2,2,3,1,2,1,2,2,2,2,3,1,2,1,2,1,3,2,2,2,2,1,3,2,2,2,2,2,2,1,2,2,2,1,3,1,2,3,2,1,2,1,3,2]OEIS Sequence A001222 - Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n)).
From OEIS A001222:
Number of prime divisors of n counted with multiplicity (also called bigomega(n) or Omega(n)). (Formerly M0094 N0031)
Sequence IDs: :a001222
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001222) |> Sequence.take!(111)
[0,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,3,1,3,2,2,1,4,2,2,3,3,1,3,1,5,2,2,2,4,1,2,2,4,1,3,1,3,3,2,1,5,2,3,2,3,1,4,2,4,2,2,1,4,1,2,3,6,2,3,1,3,2,3,1,5,1,2,3,3,2,3,1,5,4,2,1,4,2,2,2,4,1,4,2,3,2,2,2,6,1,3,3,4,1,3,1,4,3,2,1,5,1,3,2]OEIS Sequence A001227 - Number of odd divisors of n.
From OEIS A001227:
Number of odd divisors of n.
Sequence IDs: :a001227
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001227) |> Sequence.take!(105)
[1,1,2,1,2,2,2,1,3,2,2,2,2,2,4,1,2,3,2,2,4,2,2,2,3,2,4,2,2,4,2,1,4,2,4,3,2,2,4,2,2,4,2,2,6,2,2,2,3,3,4,2,2,4,4,2,4,2,2,4,2,2,6,1,4,4,2,2,4,4,2,3,2,2,6,2,4,4,2,2,5,2,2,4,4,2,4,2,2,6,4,2,4,2,4,2,2,3,6,3,2,4,2,2,8]OEIS Sequence A001333 - Numerators of continued fraction convergents to sqrt(2).
From OEIS A001333:
Numerators of continued fraction convergents to sqrt(2). (Formerly M2665 N1064)
Sequence IDs: :a001333
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001333) |> Sequence.take!(32)
[1,1,3,7,17,41,99,239,577,1393,3363,8119,19601,47321,114243,275807,665857,1607521,3880899,9369319,22619537,54608393,131836323,318281039,768398401,1855077841,4478554083,10812186007,26102926097,63018038201,152139002499,367296043199]OEIS Sequence A001358 - Semiprimes (or biprimes): products of two primes.
From OEIS A001358:
Semiprimes (or biprimes): products of two primes. (Formerly M3274 N1323)
Sequence IDs: :a001358
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001358) |> Sequence.take!(61)
[4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,55,57,58,62,65,69,74,77,82,85,86,87,91,93,94,95,106,111,115,118,119,121,122,123,129,133,134,141,142,143,145,146,155,158,159,161,166,169,177,178,183,185,187]OEIS Sequence A001405 - a(n) = binomial(n, floor(n/2)).
From OEIS A001405:
a(n) = binomial(n, floor(n/2)). (Formerly M0769 N0294)
Sequence IDs: :a001405
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001405) |> Sequence.take!(34)
[1,1,2,3,6,10,20,35,70,126,252,462,924,1716,3432,6435,12870,24310,48620,92378,184756,352716,705432,1352078,2704156,5200300,10400600,20058300,40116600,77558760,155117520,300540195,601080390,1166803110]OEIS Sequence A001477 - The nonnegative integers.
From OEIS A001477:
The nonnegative integers.
Sequence IDs: :a001477
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001477) |> Sequence.take!(78)
[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77]OEIS Sequence A001478 - The negative integers.
From OEIS A001478:
The negative integers.
Sequence IDs: :a001478
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001478) |> Sequence.take!(65)
[-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,-20,-21,-22,-23,-24,-25,-26,-27,-28,-29,-30,-31,-32,-33,-34,-35,-36,-37,-38,-39,-40,-41,-42,-43,-44,-45,-46,-47,-48,-49,-50,-51,-52,-53,-54,-55,-56,-57,-58,-59,-60,-61,-62,-63,-64,-65]OEIS Sequence A001481 - Numbers that are the sum of 2 squares.
From OEIS A001481:
Numbers that are the sum of 2 squares. (Formerly M0968 N0361)
Sequence IDs: :a001481
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001481) |> Sequence.take!(66)
[0,1,2,4,5,8,9,10,13,16,17,18,20,25,26,29,32,34,36,37,40,41,45,49,50,52,53,58,61,64,65,68,72,73,74,80,81,82,85,89,90,97,98,100,101,104,106,109,113,116,117,121,122,125,128,130,136,137,144,145,146,148,149,153,157,160]OEIS Sequence A001489 - a(n) = -n.
From OEIS A001489:
a(n) = -n.
Sequence IDs: :a001489
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001489) |> Sequence.take!(66)
[0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14,-15,-16,-17,-18,-19,-20,-21,-22,-23,-24,-25,-26,-27,-28,-29,-30,-31,-32,-33,-34,-35,-36,-37,-38,-39,-40,-41,-42,-43,-44,-45,-46,-47,-48,-49,-50,-51,-52,-53,-54,-55,-56,-57,-58,-59,-60,-61,-62,-63,-64,-65]OEIS Sequence A001511 - The ruler function: 2^a(n) divides 2n
From OEIS A001511:
The ruler function: 2^a(n) divides 2n. Or, a(n) = 2-adic valuation of 2n. (Formerly M0127 N0051)
Sequence IDs: :a001511
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001511) |> Sequence.take!(105)
[1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,6,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,7,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,5,1,2,1,3,1,2,1,4,1,2,1,3,1,2,1,6,1,2,1,3,1,2,1,4,1]OEIS Sequence A001519 - a(n) = 3*a(n-1) - a(n-2), with a(0) = a(1) = 1.
From OEIS A001519:
a(n) = 3*a(n-1) - a(n-2), with a(0) = a(1) = 1. (Formerly M1439 N0569)
Sequence IDs: :a001519
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001519) |> Sequence.take!(31)
[1,1,2,5,13,34,89,233,610,1597,4181,10946,28657,75025,196418,514229,1346269,3524578,9227465,24157817,63245986,165580141,433494437,1134903170,2971215073,7778742049,20365011074,53316291173,139583862445,365435296162,956722026041]OEIS Sequence A001615 - Dedekind psi function: n * Product_{p|n, p prime} (1 + 1/p).
From OEIS A001615:
Dedekind psi function: n * Product_{p|n, p prime} (1 + 1/p). (Formerly M2315 N0915)
Sequence IDs: :a001615
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a001615) |> Sequence.take!(69)
[1,3,4,6,6,12,8,12,12,18,12,24,14,24,24,24,18,36,20,36,32,36,24,48,30,42,36,48,30,72,32,48,48,54,48,72,38,60,56,72,42,96,44,72,72,72,48,96,56,90,72,84,54,108,72,96,80,90,60,144,62,96,96,96,84,144,68,108,96]OEIS Sequence A001699 - Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative.
From OEIS A001699:
Number of binary trees of height n; or products (ways to insert parentheses) of height n when multiplication is non-commutative and non-associative. (Formerly M3087 N1251)
Sequence IDs: :a001699
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001699) |> Sequence.take!(10)
[1,1,3,21,651,457653,210065930571,44127887745696109598901,1947270476915296449559659317606103024276803403,3791862310265926082868235028027893277370233150300118107846437701158064808916492244872560821]OEIS Sequence A001700 - a(n) = binomial(2n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1.
From OEIS A001700:
a(n) = binomial(2n+1, n+1): number of ways to put n+1 indistinguishable balls into n+1 distinguishable boxes = number of (n+1)-st degree monomials in n+1 variables = number of monotone maps from 1..n+1 to 1..n+1. (Formerly M2848 N1144)
Sequence IDs: :a001700
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001700) |> Sequence.take!(26)
[1,3,10,35,126,462,1716,6435,24310,92378,352716,1352078,5200300,20058300,77558760,300540195,1166803110,4537567650,17672631900,68923264410,269128937220,1052049481860,4116715363800,16123801841550,63205303218876,247959266474052]OEIS Sequence A001764 - a(n) = binomial(3n,n)/(2n+1) (enumerates ternary trees and also noncrossing trees).
From OEIS A001764:
a(n) = binomial(3n,n)/(2n+1) (enumerates ternary trees and also noncrossing trees). (Formerly M2926 N1174)
Sequence IDs: :a001764
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001764) |> Sequence.take!(25)
[1,1,3,12,55,273,1428,7752,43263,246675,1430715,8414640,50067108,300830572,1822766520,11124755664,68328754959,422030545335,2619631042665,16332922290300,102240109897695,642312451217745,4048514844039120,25594403741131680,162250238001816900]OEIS Sequence A001906 - F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2).
From OEIS A001906:
F(2n) = bisection of Fibonacci sequence: a(n) = 3*a(n-1) - a(n-2). (Formerly M2741 N1101)
Sequence IDs: :a001906
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001906) |> Sequence.take!(31)
[0,1,3,8,21,55,144,377,987,2584,6765,17711,46368,121393,317811,832040,2178309,5702887,14930352,39088169,102334155,267914296,701408733,1836311903,4807526976,12586269025,32951280099,86267571272,225851433717,591286729879,1548008755920]OEIS Sequence A001969 - Evil numbers: numbers with an even number of 1's in their binary expansion.
From OEIS A001969:
Evil numbers: numbers with an even number of 1's in their binary expansion. (Formerly M2395 N0952)
Sequence IDs: :a001969
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a001969) |> Sequence.take!(65)
[0,3,5,6,9,10,12,15,17,18,20,23,24,27,29,30,33,34,36,39,40,43,45,46,48,51,53,54,57,58,60,63,65,66,68,71,72,75,77,78,80,83,85,86,89,90,92,95,96,99,101,102,105,106,108,111,113,114,116,119,120,123,125,126,129]OEIS Sequence A002033 - Number of perfect partitions of n.
From OEIS A002033:
Number of perfect partitions of n. (Formerly M0131 N0053)
Sequence IDs: :a002033
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002033) |> Sequence.take!(96)
[1,1,1,2,1,3,1,4,2,3,1,8,1,3,3,8,1,8,1,8,3,3,1,20,2,3,4,8,1,13,1,16,3,3,3,26,1,3,3,20,1,13,1,8,8,3,1,48,2,8,3,8,1,20,3,20,3,3,1,44,1,3,8,32,3,13,1,8,3,13,1,76,1,3,8,8,3,13,1,48,8,3,1,44,3,3,3,20,1,44,3,8,3,3,3,112]OEIS Sequence A002106 - Number of transitive permutation groups of degree n.
From OEIS A002106:
Number of transitive permutation groups of degree n. (Formerly M1316 N0504)
Sequence IDs: :a002106
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002106) |> Sequence.take!(47)
[1,1,2,5,5,16,7,50,34,45,8,301,9,63,104,1954,10,983,8,1117,164,59,7,25000,211,96,2392,1854,8,5712,12,2801324,162,115,407,121279,11,76,306,315842,10,9491,10,2113,10923,56,6]OEIS Sequence A002110 - Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#.
From OEIS A002110:
Primorial numbers (first definition): product of first n primes. Sometimes written prime(n)#. (Formerly M1691 N0668)
Sequence IDs: :a002110
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002110) |> Sequence.take!(20)
[1,2,6,30,210,2310,30030,510510,9699690,223092870,6469693230,200560490130,7420738134810,304250263527210,13082761331670030,614889782588491410,32589158477190044730,1922760350154212639070,117288381359406970983270,7858321551080267055879090]OEIS Sequence A002113 - Palindromes in base 10.
From OEIS A002113:
Palindromes in base 10. (Formerly M0484 N0178)
Sequence IDs: :a002113
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002113) |> Sequence.take!(61)
[0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,111,121,131,141,151,161,171,181,191,202,212,222,232,242,252,262,272,282,292,303,313,323,333,343,353,363,373,383,393,404,414,424,434,444,454,464,474,484,494,505,515]OEIS Sequence A002275 - Repunits: (10^n - 1)/9. Often denoted by R_n.
From OEIS A002275:
Repunits: (10^n - 1)/9. Often denoted by R_n.
Sequence IDs: :a002275
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002275) |> Sequence.take!(21)
[0,1,11,111,1111,11111,111111,1111111,11111111,111111111,1111111111,11111111111,111111111111,1111111111111,11111111111111,111111111111111,1111111111111111,11111111111111111,111111111111111111,1111111111111111111,11111111111111111111]OEIS Sequence A002378 - Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1).
From OEIS A002378:
Oblong (or promic, pronic, or heteromecic) numbers: a(n) = n*(n+1). (Formerly M1581 N0616)
Sequence IDs: :a002378
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002378) |> Sequence.take!(51)
[0,2,6,12,20,30,42,56,72,90,110,132,156,182,210,240,272,306,342,380,420,462,506,552,600,650,702,756,812,870,930,992,1056,1122,1190,1260,1332,1406,1482,1560,1640,1722,1806,1892,1980,2070,2162,2256,2352,2450,2550]OEIS Sequence A002487 - Stern's diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2n) = a(n), a(2n+1) = a(n) + a(n+1).
From OEIS A002487:
Stern's diatomic series (or Stern-Brocot sequence): a(0) = 0, a(1) = 1; for n > 0: a(2n) = a(n), a(2n+1) = a(n) + a(n+1). (Formerly M0141 N0056)
Sequence IDs: :a002487
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002487) |> Sequence.take!(92)
[0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,6,5,9,4,11,7,10,3,11,8,13,5,12,7,9,2,9,7,12,5,13,8,11,3,10,7,11,4,9,5,6,1,7,6,11,5,14,9,13,4,15,11,18,7,17,10,13,3,14,11,19,8,21,13,18,5,17,12,19]OEIS Sequence A002530 - a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1.
From OEIS A002530:
a(n) = 4*a(n-2) - a(n-4) for n > 1, a(n) = n for n = 0, 1. (Formerly M2363 N0934)
Sequence IDs: :a002530
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002530) |> Sequence.take!(36)
[0,1,1,3,4,11,15,41,56,153,209,571,780,2131,2911,7953,10864,29681,40545,110771,151316,413403,564719,1542841,2107560,5757961,7865521,21489003,29354524,80198051,109552575,299303201,408855776,1117014753,1525870529,4168755811]OEIS Sequence A002531 - a(2n) = a(2n-1) + a(2n-2), a(2n+1) = 2a(2n) + a(2*n-1); a(0) = a(1) = 1.
From OEIS A002531:
a(2n) = a(2n-1) + a(2n-2), a(2n+1) = 2a(2n) + a(2*n-1); a(0) = a(1) = 1. (Formerly M1340 N0513)
Sequence IDs: :a002531
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002531) |> Sequence.take!(34)
[1,1,2,5,7,19,26,71,97,265,362,989,1351,3691,5042,13775,18817,51409,70226,191861,262087,716035,978122,2672279,3650401,9973081,13623482,37220045,50843527,138907099,189750626,518408351,708158977,1934726305]OEIS Sequence A002620 - Quarter-squares: floor(n/2)*ceiling(n/2). Equivalently, floor(n^2/4).
From OEIS A002620:
Quarter-squares: floor(n/2)*ceiling(n/2). Equivalently, floor(n^2/4). (Formerly M0998 N0374)
Sequence IDs: :a002620
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002620) |> Sequence.take!(58)
[0,0,1,2,4,6,9,12,16,20,25,30,36,42,49,56,64,72,81,90,100,110,121,132,144,156,169,182,196,210,225,240,256,272,289,306,324,342,361,380,400,420,441,462,484,506,529,552,576,600,625,650,676,702,729,756,784,812]OEIS Sequence A002654 - Number of ways of writing n as a sum of at most two nonzero squares, where order matters
From OEIS A002654:
Number of ways of writing n as a sum of at most two nonzero squares, where order matters; also (number of divisors of n of form 4m+1) - (number of divisors of form 4m+3). (Formerly M0012 N0001)
Sequence IDs: :a002654
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002654) |> Sequence.take!(105)
[1,1,0,1,2,0,0,1,1,2,0,0,2,0,0,1,2,1,0,2,0,0,0,0,3,2,0,0,2,0,0,1,0,2,0,1,2,0,0,2,2,0,0,0,2,0,0,0,1,3,0,2,2,0,0,0,0,2,0,0,2,0,0,1,4,0,0,2,0,0,0,1,2,2,0,0,0,0,0,2,1,2,0,0,4,0,0,0,2,2,0,0,0,0,0,0,2,1,0,3,2,0,0,2,0]OEIS Sequence A002808 - The composite numbers: numbers n of the form x*y for x > 1 and y > 1.
From OEIS A002808:
The composite numbers: numbers n of the form x*y for x > 1 and y > 1. (Formerly M3272 N1322)
Sequence IDs: :a002808
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a002808) |> Sequence.take!(64)
[4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88]OEIS Sequence A003094 - Number of unlabeled connected planar simple graphs with n nodes.
From OEIS A003094:
Number of unlabeled connected planar simple graphs with n nodes. (Formerly M1652)
Sequence IDs: :a003094
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a003094) |> Sequence.take!(13)
[1,1,1,2,6,20,99,646,5974,71885,1052805,17449299,313372298]OEIS Sequence A003418 - Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1.
From OEIS A003418:
Least common multiple (or LCM) of {1, 2, ..., n} for n >= 1, a(0) = 1. (Formerly M1590)
Sequence IDs: :a003418
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a003418) |> Sequence.take!(29)
[1,1,2,6,12,60,60,420,840,2520,2520,27720,27720,360360,360360,360360,720720,12252240,12252240,232792560,232792560,232792560,232792560,5354228880,5354228880,26771144400,26771144400,80313433200,80313433200]OEIS Sequence A003484 - Radon function, also called Hurwitz-Radon numbers.
From OEIS A003484:
Radon function, also called Hurwitz-Radon numbers. (Formerly M0161)
Sequence IDs: :a003484
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a003484) |> Sequence.take!(102)
[1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,9,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,10,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,9,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,12,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,9,1,2,1,4,1,2,1,8,1,2,1,4,1,2,1,10,1,2,1,4,1,2]OEIS Sequence A004526 - Nonnegative integers repeated, floor(n/2).
From OEIS A004526:
Nonnegative integers repeated, floor(n/2).
Sequence IDs: :a004526
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a004526) |> Sequence.take!(74)
[0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,16,16,17,17,18,18,19,19,20,20,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,35,35,36,36]OEIS Sequence A005100 - Deficient Numbers
From OEIS A005100:
Deficient numbers: numbers n such that sigma(n) < 2n. (Formerly M0514)
Sequence IDs: :a005100
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a005100) |> Sequence.take!(25)
[1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32]OEIS Sequence A005101 - Abundant Numbers
From OEIS A005101:
Abundant numbers (sum of divisors of n exceeds 2n). (Formerly M4825)
Sequence IDs: :a005101
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a005101) |> Sequence.take!(10)
[12, 18, 20, 24, 30, 36, 40, 42, 48, 54]OEIS Sequence A005117 - Squarefree numbers: numbers that are not divisible by a square greater than 1.
From OEIS A005117:
Squarefree numbers: numbers that are not divisible by a square greater than 1. (Formerly M0617)
Sequence IDs: :a005117
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a005117) |> Sequence.take!(71)
[1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,30,31,33,34,35,37,38,39,41,42,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,70,71,73,74,77,78,79,82,83,85,86,87,89,91,93,94,95,97,101,102,103,105,106,107,109,110,111,113]OEIS Sequence A005408 - The odd numbers: a(n) = 2*n + 1.
From OEIS A005408:
The odd numbers: a(n) = 2*n + 1. (Formerly M2400)
Sequence IDs: :a005408
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a005408) |> Sequence.take!(66)
[1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131]OEIS Sequence A005470 - Number of unlabeled planar simple graphs with n nodes.
From OEIS A005470:
Number of unlabeled planar simple graphs with n nodes. (Formerly M1252)
Sequence IDs: :a005470
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a005470) |> Sequence.take!(13)
[1,1,2,4,11,33,142,822,6966,79853,1140916,18681008,333312451]OEIS Sequence A005588 - Number of free binary trees admitting height n.
From OEIS A005588:
Number of free binary trees admitting height n. (Formerly M1813)
See also Counting Free Binary Trees Admitting a Given Height by Harary, et al
Sequence IDs: :a005588
Finite: True
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a005588) |> Sequence.take!(9)
[2,7,52,2133,2590407,3374951541062,5695183504479116640376509,16217557574922386301420514191523784895639577710480,131504586847961235687181874578063117114329409897550318273792033024340388219235081096658023517076950]OEIS Sequence A005811 - Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n.
From OEIS A005811:
Number of runs in binary expansion of n (n>0); number of 1's in Gray code for n. (Formerly M0110)
Sequence IDs: :a005811
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a005811) |> Sequence.take!(94)
[0,1,2,1,2,3,2,1,2,3,4,3,2,3,2,1,2,3,4,3,4,5,4,3,2,3,4,3,2,3,2,1,2,3,4,3,4,5,4,3,4,5,6,5,4,5,4,3,2,3,4,3,4,5,4,3,2,3,4,3,2,3,2,1,2,3,4,3,4,5,4,3,4,5,6,5,4,5,4,3,4,5,6,5,6,7,6,5,4,5,6,5,4,5]OEIS Sequence A005843 - The nonnegative even numbers: a(n) = 2n.
From OEIS A005843:
The nonnegative even numbers: a(n) = 2n. (Formerly M0985)
Sequence IDs: :a005843
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a005843) |> Sequence.take!(61)
[0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120]OEIS Sequence A006318 - Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers).
From OEIS A006318:
Large Schröder numbers (or large Schroeder numbers, or big Schroeder numbers). (Formerly M1659)
Sequence IDs: :a006318
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a006318) |> Sequence.take!(25)
[1,2,6,22,90,394,1806,8558,41586,206098,1037718,5293446,27297738,142078746,745387038,3937603038,20927156706,111818026018,600318853926,3236724317174,17518619320890,95149655201962,518431875418926,2832923350929742,15521467648875090]OEIS Sequence A006530 - Gpf(n): greatest prime dividing n
From OEIS A006530:
Gpf(n): greatest prime dividing n, for n >= 2; a(1)=1. (Formerly M0428)
Sequence IDs: :a006530
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a006530) |> Sequence.take!(86)
[1,2,3,2,5,3,7,2,3,5,11,3,13,7,5,2,17,3,19,5,7,11,23,3,5,13,3,7,29,5,31,2,11,17,7,3,37,19,13,5,41,7,43,11,5,23,47,3,7,5,17,13,53,3,11,7,19,29,59,5,61,31,7,2,13,11,67,17,23,7,71,3,73,37,5,19,11,13,79,5,3,41,83,7,17,43]OEIS Sequence A006882 - Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1.
From OEIS A006882:
Double factorials n!!: a(n) = n*a(n-2) for n > 1, a(0) = a(1) = 1. (Formerly M0876)
Sequence IDs: :a006882
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a006882) |> Sequence.take!(27)
[1,1,2,3,8,15,48,105,384,945,3840,10395,46080,135135,645120,2027025,10321920,34459425,185794560,654729075,3715891200,13749310575,81749606400,316234143225,1961990553600,7905853580625,51011754393600]OEIS Sequence A006894 - Number of planted 3-trees of height < n.
From OEIS A006894:
Number of planted 3-trees of height < n. (Formerly M1254)
Sequence IDs: :a006894
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a006894) |> Sequence.take!(11)
[1,2,4,11,67,2279,2598061,3374961778892,5695183504492614029263279,16217557574922386301420536972254869595782763547561,131504586847961235687181874578063117114329409897615188504091716162522225834932122128288032336298142]OEIS Sequence A006966 - Number of lattices on n unlabeled nodes.
From OEIS A006966:
Number of lattices on n unlabeled nodes. (Formerly M1486)
Sequence IDs: :a006966
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a006966) |> Sequence.take!(21)
[1,1,1,1,2,5,15,53,222,1078,5994,37622,262776,2018305,16873364,152233518,1471613387,15150569446,165269824761,1901910625578,23003059864006]OEIS Sequence A007318 - Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n.
From OEIS A007318:
Pascal's triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n. (Formerly M0082)
Sequence IDs: :a007318
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a007318) |> Sequence.take!(78)
[1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,10,10,5,1,1,6,15,20,15,6,1,1,7,21,35,35,21,7,1,1,8,28,56,70,56,28,8,1,1,9,36,84,126,126,84,36,9,1,1,10,45,120,210,252,210,120,45,10,1,1,11,55,165,330,462,462,330,165,55,11,1]OEIS Sequence A008277 - Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
From OEIS A008277:
Triangle of Stirling numbers of the second kind, S2(n,k), n >= 1, 1 <= k <= n.
Sequence IDs: :a008277
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a008277) |> Sequence.take!(66)
[1,1,1,1,3,1,1,7,6,1,1,15,25,10,1,1,31,90,65,15,1,1,63,301,350,140,21,1,1,127,966,1701,1050,266,28,1,1,255,3025,7770,6951,2646,462,36,1,1,511,9330,34105,42525,22827,5880,750,45,1,1,1023,28501,145750,246730,179487,63987,11880,1155,55,1]OEIS Sequence A008279 - Triangle T(n,k) = n!/(n-k)! (0 <= k <= n) read by rows, giving number of permutations of n things k at a time.
From OEIS A008279:
Triangle T(n,k) = n!/(n-k)! (0 <= k <= n) read by rows, giving number of permutations of n things k at a time.
Sequence IDs: :a008279
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a008279) |> Sequence.take!(55)
[1,1,1,1,2,2,1,3,6,6,1,4,12,24,24,1,5,20,60,120,120,1,6,30,120,360,720,720,1,7,42,210,840,2520,5040,5040,1,8,56,336,1680,6720,20160,40320,40320,1,9,72,504,3024,15120,60480,181440,362880,362880]OEIS Sequence A008292 - Triangle of Eulerian numbers T(n,k) (n >= 1, 1 <= k <= n) read by rows.
From OEIS A008292:
Triangle of Eulerian numbers T(n,k) (n >= 1, 1 <= k <= n) read by rows.
Sequence IDs: :a008292
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a008292) |> Sequence.take!(55)
[1,1,1,1,4,1,1,11,11,1,1,26,66,26,1,1,57,302,302,57,1,1,120,1191,2416,1191,120,1,1,247,4293,15619,15619,4293,247,1,1,502,14608,88234,156190,88234,14608,502,1,1,1013,47840,455192,1310354,1310354,455192,47840,1013,1]OEIS Sequence A008683 - Möbius (or Moebius) function mu(n)
From OEIS A008683:
Möbius (or Moebius) function mu(n). mu(1) = 1; mu(n) = (-1)^k if n is the product of k different primes; otherwise mu(n) = 0.
Sequence IDs: :a008683
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a008683) |> Sequence.take!(78)
[1,-1,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,1,0,-1,0,-1,0,1,1,-1,0,0,1,0,0,-1,-1,-1,0,1,1,1,0,-1,1,1,0,-1,-1,-1,0,0,1,-1,0,0,0,1,0,-1,0,1,0,1,1,-1,0,-1,1,0,0,1,-1,-1,0,1,-1,-1,0,-1,1,0,0,1,-1]OEIS Sequence A018252 - The nonprime numbers: 1 together with the composite numbers, A002808.
From OEIS A018252:
The nonprime numbers: 1 together with the composite numbers, A002808.
Sequence IDs: :a018252
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a018252) |> Sequence.take!(65)
[1,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88]OEIS Sequence A020639 - Lpf(n): least prime dividing
From OEIS A020639:
Lpf(n): least prime dividing n (when n > 1); a(1) = 1.
Sequence IDs: :a020639
Finite: False
Offset: 1
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a020639) |> Sequence.take!(97)
[1,2,3,2,5,2,7,2,3,2,11,2,13,2,3,2,17,2,19,2,3,2,23,2,5,2,3,2,29,2,31,2,3,2,5,2,37,2,3,2,41,2,43,2,3,2,47,2,7,2,3,2,53,2,5,2,3,2,59,2,61,2,3,2,5,2,67,2,3,2,71,2,73,2,3,2,7,2,79,2,3,2,83,2,5,2,3,2,89,2,7,2,3,2,5,2,97]OEIS Sequence A027642 - Denominator of Bernoulli number B_n.
From OEIS A027642:
Denominator of Bernoulli number B_n.
Sequence IDs: :a027642
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a027642) |> Sequence.take!(62)
[1,2,6,1,30,1,42,1,30,1,66,1,2730,1,6,1,510,1,798,1,330,1,138,1,2730,1,6,1,870,1,14322,1,510,1,6,1,1919190,1,6,1,13530,1,1806,1,690,1,282,1,46410,1,66,1,1590,1,798,1,870,1,354,1,56786730,1]OEIS Sequence A049310 - Triangle of coefficients of Chebyshev's S(n,x) := U(n,x/2) polynomials (exponents in increasing order).
From OEIS A049310:
Triangle of coefficients of Chebyshev's S(n,x) := U(n,x/2) polynomials (exponents in increasing order).
Sequence IDs: :a049310
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a049310) |> Sequence.take!(86)
[1,0,1,-1,0,1,0,-2,0,1,1,0,-3,0,1,0,3,0,-4,0,1,-1,0,6,0,-5,0,1,0,-4,0,10,0,-6,0,1,1,0,-10,0,15,0,-7,0,1,0,5,0,-20,0,21,0,-8,0,1,-1,0,15,0,-35,0,28,0,-9,0,1,0,-6,0,35,0,-56,0,36,0,-10,0,1,1,0,-21,0,70,0,-84,0]OEIS Sequence A055512 - Lattices with n labeled elements.
From OEIS A055512:
Lattices with n labeled elements.
Sequence IDs: :a055512
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a055512) |> Sequence.take!(19)
[1,1,2,6,36,380,6390,157962,5396888,243179064,13938711210,987858368750,84613071940452,8597251494954564,1020353444641839854,139627532137612581090,21788453795572514675760,3840596246648027262079472,758435490711709577216754642]OEIS Sequence A070939 - Length of binary representation of n.
From OEIS A070939:
Length of binary representation of n.
Sequence IDs: :a070939
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a070939) |> Sequence.take!(105)
[1,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7]OEIS Sequence A074206 - Kalmár's [Kalmar's] problem: number of ordered factorizations of n.
From OEIS A074206:
Kalmár's [Kalmar's] problem: number of ordered factorizations of n.
Sequence IDs: :a074206
Finite: False
Offset: 0
Example
iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Core, :a074206) |> Sequence.take!(97)
[0,1,1,1,2,1,3,1,4,2,3,1,8,1,3,3,8,1,8,1,8,3,3,1,20,2,3,4,8,1,13,1,16,3,3,3,26,1,3,3,20,1,13,1,8,8,3,1,48,2,8,3,8,1,20,3,20,3,3,1,44,1,3,8,32,3,13,1,8,3,13,1,76,1,3,8,8,3,13,1,48,8,3,1,44,3,3,3,20,1,44,3,8,3,3,3,112]