chunky

v0.12.0

chunky v0.12.0 Chunky.Sequence.OEIS.Factors View Source

OEIS Sequences dealing with Factors, Factorization, and properties of integer factors.

Available Sequences

Link to this section Summary

Functions

create_sequence_a000037(opts)

OEIS Sequence A000037 - Numbers that are not squares (or, the nonsquares).

create_sequence_a000977(opts)

OEIS Sequence A000977 - Numbers that are divisible by at least three different primes.

create_sequence_a001414(opts)

OEIS Sequence A001414 - Integer log of n: sum of primes dividing n (with repetition). Also called sopfr(n).

create_sequence_a001597(opts)

OEIS Sequence A001597 - Perfect Powers

create_sequence_a001694(opts)

OEIS Sequence A001694 - Powerful Numbers

create_sequence_a001826(opts)

OEIS Sequence A001826 - Number of divisors of n of form 4k+1.

create_sequence_a001842(opts)

OEIS Sequence A001842 - Expansion of Sum_{n>=0} x^(4n+3)/(1 - x^(4n+3)).

create_sequence_a002182(opts)

OEIS Sequence A002182 - Highly composite numbers: numbers with record value

create_sequence_a002473(opts)

OEIS Sequence A002473 - 7-smooth Numbers

create_sequence_a003586(opts)

OEIS Sequence A003586 - 3-smooth Numbers

create_sequence_a004709(opts)

OEIS Sequence A004709 - Cubefree numbers: numbers that are not divisible by any cube > 1.

create_sequence_a005361(opts)

OEIS Sequence A005361 - Product of Expoenents of prime factors of N

create_sequence_a005934(opts)

OEIS Sequence A005934 - Highly powerful numbers: numbers with record value

create_sequence_a006881(opts)

OEIS Sequence A006881 - Squarefree semiprimes: Numbers that are the product of two distinct primes.

create_sequence_a007018(opts)

OEIS Sequence A007018 - a(n) = a(n-1)^2 + a(n-1), a(0)=1.

create_sequence_a007304(opts)

OEIS Sequence A007304 - Sphenic numbers: products of 3 distinct primes.

create_sequence_a007412(opts)

OEIS Sequence A007412 - The noncubes: n + [ (n + [ n^{1/3} ])^{1/3} ].

create_sequence_a007434(opts)

OEIS Sequence A007434 - Jordan function J_2(n)

create_sequence_a007774(opts)

OEIS Sequence A007774 - Numbers that are divisible by exactly 2 different primes.

create_sequence_a007947(opts)

OEIS Sequence A007947 - Largest squarefree number dividing n: the squarefree kernel of n, rad(n), radical of n.

create_sequence_a008966(opts)

OEIS Sequence A008966 - 1 if n is squarefree, else 0.

create_sequence_a013929(opts)

OEIS Sequence A013929 - Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117.

create_sequence_a014612(opts)

OEIS Sequence A014612 - Numbers that are the product of exactly three primes.

create_sequence_a014613(opts)

OEIS Sequence A014613 - Numbers that are products of 4 primes

create_sequence_a014614(opts)

OEIS Sequence A014614 - Numbers that are products of 5 primes

create_sequence_a018253(opts)

OEIS Sequence A018253 - Divisors of 24.

create_sequence_a018256(opts)

OEIS Sequence A018256 - Divisors of 36.

create_sequence_a018261(opts)

OEIS Sequence A018261 - Divisors of 48.

create_sequence_a018266(opts)

OEIS Sequence A018266 - Divisors of 60.

create_sequence_a018293(opts)

OEIS Sequence A018293 - Divisors of 120.

create_sequence_a018321(opts)

OEIS Sequence A018321 - Divisors of 180.

create_sequence_a018350(opts)

OEIS Sequence A018350 - Divisors of 240.

create_sequence_a018412(opts)

OEIS Sequence A018412 - Divisors of 360.

create_sequence_a018609(opts)

OEIS Sequence A018609 - Divisors of 720.

create_sequence_a018676(opts)

OEIS Sequence A018676 - Divisors of 840.

create_sequence_a030513(opts)

OEIS Sequence A030513 - Numbers with 4 divisors.

create_sequence_a030515(opts)

OEIS Sequence A030515 - Numbers with exactly 6 divisors.

create_sequence_a033273(opts)

OEIS Sequence A033273 - Number of nonprime divisors of n.

create_sequence_a033942(opts)

OEIS Sequence A033942 - At least 3 prime factors (counted with multiplicity).

create_sequence_a033987(opts)

OEIS Sequence A033987 - Numbers that are divisible by at least 4 primes (counted with multiplicity).

create_sequence_a033992(opts)

OEIS Sequence A033992 - Numbers that are divisible by exactly three different primes.

create_sequence_a033993(opts)

OEIS Sequence A033993 - Numbers that are divisible by exactly four different primes.

create_sequence_a036537(opts)

OEIS Sequence A036537 - Numbers whose number of divisors is a power of 2.

create_sequence_a037143(opts)

OEIS Sequence A037143 - Numbers with at most 2 prime factors (counted with multiplicity).

create_sequence_a038109(opts)

OEIS Sequence A038109 - Divisible exactly by the square of a prime.

create_sequence_a039956(opts)

OEIS Sequence A039956 - Even squarefree numbers.

create_sequence_a046099(opts)

OEIS Sequence A046099 - Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709.

create_sequence_a046306(opts)

OEIS Sequence A046306 - Numbers that are divisible by exactly 6 primes with multiplicity.

create_sequence_a046308(opts)

OEIS Sequence A046308 - Numbers that are divisible by exactly 7 primes counting multiplicity.

create_sequence_a046310(opts)

OEIS Sequence A046310 - Numbers that are divisible by exactly 8 primes counting multiplicity.

create_sequence_a046312(opts)

OEIS Sequence A046312 - Numbers that are divisible by exactly 9 primes with multiplicity.

create_sequence_a046314(opts)

OEIS Sequence A046314 - Numbers that are divisible by exactly 10 primes with multiplicity.

create_sequence_a046321(opts)

OEIS Sequence A046321 - Odd numbers divisible by exactly 8 primes (counted with multiplicity).

create_sequence_a046386(opts)

OEIS Sequence A046386 - Products of four distinct primes.

create_sequence_a046387(opts)

OEIS Sequence A046387 - Products of 5 distinct primes.

create_sequence_a046660(opts)

OEIS Sequence A046660 - Excess of n = number of prime divisors (with multiplicity) - number of prime divisors (without multiplicity).

create_sequence_a046758(opts)

OEIS Sequence A046758 - Equidigital numbers.

create_sequence_a046759(opts)

OEIS Sequence A046759 - Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n).

create_sequence_a046760(opts)

OEIS Sequence A046760 - Wasteful numbers.

create_sequence_a048272(opts)

OEIS Sequence A048272 - Number of odd divisors of n minus number of even divisors of n.

create_sequence_a051037(opts)

OEIS Sequence A051037 - 5-smooth Numbers

create_sequence_a051038(opts)

OEIS Sequence A051038 - 11-smooth Numbers

create_sequence_a051270(opts)

OEIS Sequence A051270 - Numbers that are divisible by exactly 5 different primes.

create_sequence_a052486(opts)

OEIS Sequence A052486 - Achilles numbers - powerful but imperfect

create_sequence_a056911(opts)

OEIS Sequence A056911 - Odd squarefree numbers.

create_sequence_a059269(opts)

OEIS Sequence A059269 - Numbers n for which the number of divisors, tau(n), is divisible by 3.

create_sequence_a059376(opts)

OEIS Sequence A059376 - Jordan function J_3(n).

create_sequence_a059377(opts)

OEIS Sequence A059377 - Jordan function J_4(n).

create_sequence_a059378(opts)

OEIS Sequence A059378 - Jordan function J_5(n).

create_sequence_a065958(opts)

OEIS Sequence A065958 - a(n) = n^2*Product_{distinct primes p dividing n} (1+1/p^2).

create_sequence_a065959(opts)

OEIS Sequence A065959 - a(n) = n^3*Product_{distinct primes p dividing n} (1+1/p^3).

create_sequence_a065960(opts)

OEIS Sequence A065960 - a(n) = n^4*Product_{distinct primes p dividing n} (1+1/p^4).

create_sequence_a067259(opts)

OEIS Sequence A067259 - Cubefree numbers which are not squarefree.

create_sequence_a067885(opts)

OEIS Sequence A067885 - Product of 6 distinct primes.

create_sequence_a069091(opts)

OEIS Sequence A069091 - Jordan function J_6(n).

create_sequence_a069092(opts)

OEIS Sequence A069092 - Jordan function J_7(n).

create_sequence_a069093(opts)

OEIS Sequence A069093 - Jordan function J_8(n).

create_sequence_a069094(opts)

OEIS Sequence A069094 - Jordan function J_9(n).

create_sequence_a069095(opts)

OEIS Sequence A069095 - Jordan function J_10(n).

create_sequence_a069272(opts)

OEIS Sequence A069272 - 11-almost primes (generalization of semiprimes).

create_sequence_a069273(opts)

OEIS Sequence A069273 - 12-almost primes (generalization of semiprimes).

create_sequence_a069274(opts)

OEIS Sequence A069274 - 13-almost primes (generalization of semiprimes).

create_sequence_a069275(opts)

OEIS Sequence A069275 - 14-almost primes (generalization of semiprimes).

create_sequence_a069276(opts)

OEIS Sequence A069276 - 15-almost primes (generalization of semiprimes).

create_sequence_a069277(opts)

OEIS Sequence A069277 - 16-almost primes (generalization of semiprimes).

create_sequence_a069278(opts)

OEIS Sequence A069278 - 17-almost primes (generalization of semiprimes).

create_sequence_a069279(opts)

OEIS Sequence A069279 - Products of exactly 18 primes (generalization of semiprimes).

create_sequence_a069280(opts)

OEIS Sequence A069280 - 19-almost primes (generalization of semiprimes).

create_sequence_a069281(opts)

OEIS Sequence A069281 - 20-almost primes (generalization of semiprimes).

create_sequence_a074969(opts)

OEIS Sequence A074969 - Numbers with six distinct prime divisors.

create_sequence_a076479(opts)

OEIS Sequence A076479 - a(n) = mu(rad(n)), where mu is the Moebius-function

create_sequence_a080197(opts)

OEIS Sequence A080197 - 13-smooth Numbers

create_sequence_a080681(opts)

OEIS Sequence A080681 - 17-smooth Numbers

create_sequence_a080682(opts)

OEIS Sequence A080682 - 19-smooth Numbers

create_sequence_a080683(opts)

OEIS Sequence A080683 - 23-smooth Numbers

create_sequence_a117805(opts)

OEIS Sequence A117805 - Start with 3. Square the previous term and subtract it.

create_sequence_a123321(opts)

OEIS Sequence A123321 - Products of 7 distinct primes (squarefree 7-almost primes).

create_sequence_a123322(opts)

OEIS Sequence A123322 - Products of 8 distinct primes (squarefree 8-almost primes).

create_sequence_a130897(opts)

OEIS Sequence A130897 - Numbers that are not exponentially squarefree.

create_sequence_a160889(opts)

OEIS Sequence A160889 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4.

create_sequence_a160891(opts)

OEIS Sequence A160891 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 5.

create_sequence_a160893(opts)

OEIS Sequence A160893 - a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n).

create_sequence_a160895(opts)

OEIS Sequence A160895 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7.

create_sequence_a160897(opts)

OEIS Sequence A160897 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8.

create_sequence_a160908(opts)

OEIS Sequence A160908 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 9.

create_sequence_a160953(opts)

OEIS Sequence A160953 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10.

create_sequence_a160957(opts)

OEIS Sequence A160957 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11.

create_sequence_a160960(opts)

OEIS Sequence A160960 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 12.

create_sequence_a162643(opts)

OEIS Sequence A162643 - Numbers such that their number of divisors is not a power of 2.

create_sequence_a165412(opts)

OEIS Sequence A165412 - Divisors of 2520.

create_sequence_a178858(opts)

OEIS Sequence A178858 - Divisors of 5040.

create_sequence_a178859(opts)

OEIS Sequence A178859 - Divisors of 7560.

create_sequence_a178860(opts)

OEIS Sequence A178860 - Divisors of 10080.

create_sequence_a178861(opts)

OEIS Sequence A178861 - Divisors of 15120.

create_sequence_a178862(opts)

OEIS Sequence A178862 - Divisors of 20160.

create_sequence_a178863(opts)

OEIS Sequence A178863 - Divisors of 25200.

create_sequence_a178864(opts)

OEIS Sequence A178864 - Divisors of 27720.

create_sequence_a178877(opts)

OEIS Sequence A178877 - Divisors of 1260.

create_sequence_a178878(opts)

OEIS Sequence A178878 - Divisors of 1680.

create_sequence_a209061(opts)

OEIS Sequence A209061 - Exponentially squarefree numbers.

create_sequence_a211337(opts)

OEIS Sequence A211337 - Numbers n for which the number of divisors, tau(n), is congruent to 1 modulo 3.

create_sequence_a211338(opts)

OEIS Sequence A211338 - Numbers n for which the number of divisors, tau(n), is congruent to 2 modulo 3.

seq_a000037(idx, last)
seq_a000977(idx, last)
seq_a001414(idx)
seq_a001597(idx, last)
seq_a001694(idx, last)
seq_a001826(idx)
seq_a001842(idx)
seq_a002473(idx, last)
seq_a003586(idx, last)
seq_a004709(idx, last)
seq_a005361(idx)
seq_a006881(idx, last)
seq_a007018(idx, last)
seq_a007304(idx, last)
seq_a007412(idx, last)
seq_a007434(idx)
seq_a007774(idx, last)
seq_a007947(idx)
seq_a008966(idx)
seq_a013929(idx, last)
seq_a014612(idx, last)
seq_a014613(idx, last)
seq_a014614(idx, last)
seq_a030513(idx, last)
seq_a030515(idx, last)
seq_a033273(idx)
seq_a033942(idx, last)
seq_a033987(idx, last)
seq_a033992(idx, last)
seq_a033993(idx, last)
seq_a036537(idx, last)
seq_a037143(idx, last)
seq_a038109(idx, last)
seq_a039956(idx, last)
seq_a046099(idx, last)
seq_a046306(idx, last)
seq_a046308(idx, last)
seq_a046310(idx, last)
seq_a046312(idx, last)
seq_a046314(idx, last)
seq_a046321(idx, last)
seq_a046386(idx, last)
seq_a046387(idx, last)
seq_a046660(idx)
seq_a046758(idx, last)
seq_a046759(idx, last)
seq_a046760(idx, last)
seq_a048272(idx)
seq_a051037(idx, last)
seq_a051038(idx, last)
seq_a051270(idx, last)
seq_a052486(idx, last)
seq_a056911(idx, last)
seq_a059269(idx, last)
seq_a059376(idx)
seq_a059377(idx)
seq_a059378(idx)
seq_a065958(idx)
seq_a065959(idx)
seq_a065960(idx)
seq_a067259(idx, last)
seq_a067885(idx, last)
seq_a069091(idx)
seq_a069092(idx)
seq_a069093(idx)
seq_a069094(idx)
seq_a069095(idx)
seq_a069272(idx, last)
seq_a069273(idx, last)
seq_a069274(idx, last)
seq_a069275(idx, last)
seq_a069276(idx, last)
seq_a069277(idx, last)
seq_a069278(idx, last)
seq_a069279(idx, last)
seq_a069280(idx, last)
seq_a069281(idx, last)
seq_a074969(idx, last)
seq_a076479(idx)
seq_a080197(idx, last)
seq_a080681(idx, last)
seq_a080682(idx, last)
seq_a080683(idx, last)
seq_a117805(idx, last)
seq_a123321(idx, last)
seq_a123322(idx, last)
seq_a130897(idx, last)
seq_a160889(idx)
seq_a160891(idx)
seq_a160893(idx)
seq_a160895(idx)
seq_a160897(idx)
seq_a160908(idx)
seq_a160953(idx)
seq_a160957(idx)
seq_a160960(idx)
seq_a162643(idx, last)
seq_a209061(idx, last)
seq_a211337(idx, last)
seq_a211338(idx, last)

Link to this section Functions

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create_sequence_a000037(opts)

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OEIS Sequence A000037 - Numbers that are not squares (or, the nonsquares).

From OEIS A000037:

Numbers that are not squares (or, the nonsquares). (Formerly M0613 N0223)

Sequence IDs: :a000037

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a000037) |> Sequence.take!(90)
[2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,27,28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,50,51,52,53,54,55,56,57,58,59,60,61,62,63,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99]
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create_sequence_a000977(opts)

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OEIS Sequence A000977 - Numbers that are divisible by at least three different primes.

From OEIS A000977:

Numbers that are divisible by at least three different primes.

Sequence IDs: :a000977

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a000977) |> Sequence.take!(50)
[30,42,60,66,70,78,84,90,102,105,110,114,120,126,130,132,138,140,150,154,156,165,168,170,174,180,182,186,190,195,198,204,210,220,222,228,230,231,234,238,240,246,252,255,258,260,264,266,270,273]
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create_sequence_a001414(opts)

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OEIS Sequence A001414 - Integer log of n: sum of primes dividing n (with repetition). Also called sopfr(n).

From OEIS A001414:

Integer log of n: sum of primes dividing n (with repetition). Also called sopfr(n). (Formerly M0461 N0168)

Sequence IDs: :a001414

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a001414) |> Sequence.take!(78)
[0,2,3,4,5,5,7,6,6,7,11,7,13,9,8,8,17,8,19,9,10,13,23,9,10,15,9,11,29,10,31,10,14,19,12,10,37,21,16,11,41,12,43,15,11,25,47,11,14,12,20,17,53,11,16,13,22,31,59,12,61,33,13,12,18,16,67,21,26,14,71,12,73,39,13,23,18,18]
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create_sequence_a001597(opts)

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OEIS Sequence A001597 - Perfect Powers

From OEIS A001597:

Perfect powers: m^k where m > 0 and k >= 2. (Formerly M3326 N1336)

Sequence IDs: :a001597

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a001597) |> Sequence.take!(20)
[1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 169, 196, 216]
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create_sequence_a001694(opts)

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OEIS Sequence A001694 - Powerful Numbers

From OEIS A001694:

Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers). (Formerly M3325 N1335)

Sequence IDs: :a001694

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a001694) |> Sequence.take!(20)
[1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169]
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create_sequence_a001826(opts)

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OEIS Sequence A001826 - Number of divisors of n of form 4k+1.

From OEIS A001826:

Number of divisors of n of form 4k+1. (Formerly )

Sequence IDs: :a001826

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a001826) |> Sequence.take!(105)
[1,1,1,1,2,1,1,1,2,2,1,1,2,1,2,1,2,2,1,2,2,1,1,1,3,2,2,1,2,2,1,1,2,2,2,2,2,1,2,2,2,2,1,1,4,1,1,1,2,3,2,2,2,2,2,1,2,2,1,2,2,1,3,1,4,2,1,2,2,2,1,2,2,2,3,1,2,2,1,2,3,2,1,2,4,1,2,1,2,4,2,1,2,1,2,1,2,2,3,3,2,2,1,2,4]
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create_sequence_a001842(opts)

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OEIS Sequence A001842 - Expansion of Sum_{n>=0} x^(4n+3)/(1 - x^(4n+3)).

From OEIS A001842:

Expansion of Sum_{n>=0} x^(4n+3)/(1 - x^(4n+3)). (Formerly )

Sequence IDs: :a001842

Finite: False

Offset: 0

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a001842) |> Sequence.take!(87)
[0,0,0,1,0,0,1,1,0,1,0,1,1,0,1,2,0,0,1,1,0,2,1,1,1,0,0,2,1,0,2,1,0,2,0,2,1,0,1,2,0,0,2,1,1,2,1,1,1,1,0,2,0,0,2,2,1,2,0,1,2,0,1,3,0,0,2,1,0,2,2,1,1,0,0,3,1,2,2,1,0,2,0,1,2,0,1]
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create_sequence_a002182(opts)

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OEIS Sequence A002182 - Highly composite numbers: numbers with record value

From OEIS A002182:

Highly composite numbers, definition (1): where d(n), the number of divisors of n (A000005), increases to a record. (Formerly M1025 N0385)

Sequence IDs: :a002182

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a002182) |> Sequence.take!(20)
[1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560]
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create_sequence_a002473(opts)

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OEIS Sequence A002473 - 7-smooth Numbers

From OEIS A002473:

7-smooth numbers: positive numbers whose prime divisors are all <= 7. (Formerly M0477 N0177)

Sequence IDs: :a002473

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a002473) |> Sequence.drop(20) |> Sequence.take!(20)
[28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80]
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create_sequence_a003586(opts)

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OEIS Sequence A003586 - 3-smooth Numbers

From OEIS A003586:

3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0.

Sequence IDs: :a003586

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a003586) |> Sequence.drop(20) |> Sequence.take!(20)
[108, 128, 144, 162, 192, 216, 243, 256, 288, 324, 384, 432, 486, 512, 576, 648, 729, 768, 864, 972]
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create_sequence_a004709(opts)

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OEIS Sequence A004709 - Cubefree numbers: numbers that are not divisible by any cube > 1.

From OEIS A004709:

Cubefree numbers: numbers that are not divisible by any cube > 1. (Formerly )

Sequence IDs: :a004709

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a004709) |> Sequence.take!(72)
[1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,25,26,28,29,30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,55,57,58,59,60,61,62,63,65,66,67,68,69,70,71,73,74,75,76,77,78,79,82,83,84,85]
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create_sequence_a005361(opts)

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OEIS Sequence A005361 - Product of Expoenents of prime factors of N

From OEIS A005361:

Product of exponents of prime factorization of n. (Formerly M0063)

Sequence IDs: :a005361

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a005361) |> Sequence.take!(20)
[1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2]
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create_sequence_a005934(opts)

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OEIS Sequence A005934 - Highly powerful numbers: numbers with record value

From OEIS A005934:

Highly powerful numbers: numbers with record value of the product of the exponents in prime factorization (A005361). (Formerly M3333)

Sequence IDs: :a005934

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a005934) |> Sequence.take!(20)
[1, 4, 8, 16, 32, 64, 128, 144, 216, 288, 432, 864, 1296, 1728, 2592, 3456, 5184, 7776, 10368, 15552]
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create_sequence_a006881(opts)

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OEIS Sequence A006881 - Squarefree semiprimes: Numbers that are the product of two distinct primes.

From OEIS A006881:

Squarefree semiprimes: Numbers that are the product of two distinct primes. (Formerly M4082)

Sequence IDs: :a006881

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a006881) |> Sequence.take!(60)
[6,10,14,15,21,22,26,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,82,85,86,87,91,93,94,95,106,111,115,118,119,122,123,129,133,134,141,142,143,145,146,155,158,159,161,166,177,178,183,185,187,194,201,202,203,205]
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create_sequence_a007018(opts)

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OEIS Sequence A007018 - a(n) = a(n-1)^2 + a(n-1), a(0)=1.

From OEIS A007018:

a(n) = a(n-1)^2 + a(n-1), a(0)=1. (Formerly M1713)

Sequence IDs: :a007018

Finite: False

Offset: 0

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a007018) |> Sequence.take!(9)
[1,2,6,42,1806,3263442,10650056950806,113423713055421844361000442,12864938683278671740537145998360961546653259485195806]
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create_sequence_a007304(opts)

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OEIS Sequence A007304 - Sphenic numbers: products of 3 distinct primes.

From OEIS A007304:

Sphenic numbers: products of 3 distinct primes. (Formerly M5207)

Sequence IDs: :a007304

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a007304) |> Sequence.take!(53)
[30,42,66,70,78,102,105,110,114,130,138,154,165,170,174,182,186,190,195,222,230,231,238,246,255,258,266,273,282,285,286,290,310,318,322,345,354,357,366,370,374,385,399,402,406,410,418,426,429,430,434,435,438]
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create_sequence_a007412(opts)

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OEIS Sequence A007412 - The noncubes: n + [ (n + [ n^{1/3} ])^{1/3} ].

From OEIS A007412:

The noncubes: n + [ (n + [ n^{1/3} ])^{1/3} ]. (Formerly M0493)

Sequence IDs: :a007412

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a007412) |> Sequence.take!(54)
[2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57]
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create_sequence_a007434(opts)

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OEIS Sequence A007434 - Jordan function J_2(n)

From OEIS A007434:

Jordan function J_2(n) (a generalization of phi(n)). (Formerly M2717)

Sequence IDs: :a007434

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a007434) |> Sequence.take!(48)
[1,3,8,12,24,24,48,48,72,72,120,96,168,144,192,192,288,216,360,288,384,360,528,384,600,504,648,576,840,576,960,768,960,864,1152,864,1368,1080,1344,1152,1680,1152,1848,1440,1728,1584,2208,1536]
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create_sequence_a007774(opts)

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OEIS Sequence A007774 - Numbers that are divisible by exactly 2 different primes.

From OEIS A007774:

Numbers that are divisible by exactly 2 different primes.

Sequence IDs: :a007774

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a007774) |> Sequence.take!(65)
[6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,44,45,46,48,50,51,52,54,55,56,57,58,62,63,65,68,69,72,74,75,76,77,80,82,85,86,87,88,91,92,93,94,95,96,98,99,100,104,106,108,111,112,115,116,117,118]
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create_sequence_a007947(opts)

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OEIS Sequence A007947 - Largest squarefree number dividing n: the squarefree kernel of n, rad(n), radical of n.

From OEIS A007947:

Largest squarefree number dividing n: the squarefree kernel of n, rad(n), radical of n.

Sequence IDs: :a007947

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a007947) |> Sequence.take!(78)
[1,2,3,2,5,6,7,2,3,10,11,6,13,14,15,2,17,6,19,10,21,22,23,6,5,26,3,14,29,30,31,2,33,34,35,6,37,38,39,10,41,42,43,22,15,46,47,6,7,10,51,26,53,6,55,14,57,58,59,30,61,62,21,2,65,66,67,34,69,70,71,6,73,74,15,38,77,78]
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create_sequence_a008966(opts)

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OEIS Sequence A008966 - 1 if n is squarefree, else 0.

From OEIS A008966:

1 if n is squarefree, else 0. (Formerly )

Sequence IDs: :a008966

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a008966) |> Sequence.take!(100)
[1,1,1,0,1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,1,0,0,1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
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create_sequence_a013929(opts)

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OEIS Sequence A013929 - Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117.

From OEIS A013929:

Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117.

Sequence IDs: :a013929

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a013929) |> Sequence.take!(62)
[4,8,9,12,16,18,20,24,25,27,28,32,36,40,44,45,48,49,50,52,54,56,60,63,64,68,72,75,76,80,81,84,88,90,92,96,98,99,100,104,108,112,116,117,120,121,124,125,126,128,132,135,136,140,144,147,148,150,152,153,156,160]
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create_sequence_a014612(opts)

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OEIS Sequence A014612 - Numbers that are the product of exactly three primes.

From OEIS A014612:

Numbers that are the product of exactly three (not necessarily distinct) primes. (Formerly )

Sequence IDs: :a014612

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a014612) |> Sequence.take!(57)
[8,12,18,20,27,28,30,42,44,45,50,52,63,66,68,70,75,76,78,92,98,99,102,105,110,114,116,117,124,125,130,138,147,148,153,154,164,165,170,171,172,174,175,182,186,188,190,195,207,212,222,230,231,236,238,242,244]
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create_sequence_a014613(opts)

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OEIS Sequence A014613 - Numbers that are products of 4 primes

From OEIS A014613:

Numbers that are products of 4 primes (these numbers are sometimes called "4-almost primes", a generalization of semiprimes).

Sequence IDs: :a014613

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a014613) |> Sequence.take!(54)
[16,24,36,40,54,56,60,81,84,88,90,100,104,126,132,135,136,140,150,152,156,184,189,196,198,204,210,220,225,228,232,234,248,250,260,276,294,296,297,306,308,315,328,330,340,342,344,348,350,351,364,372,375,376]
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create_sequence_a014614(opts)

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OEIS Sequence A014614 - Numbers that are products of 5 primes

From OEIS A014614:

Numbers that are products of 5 primes (or 5-almost primes, a generalization of semiprimes).

Sequence IDs: :a014614

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a014614) |> Sequence.take!(52)
[32,48,72,80,108,112,120,162,168,176,180,200,208,243,252,264,270,272,280,300,304,312,368,378,392,396,405,408,420,440,450,456,464,468,496,500,520,552,567,588,592,594,612,616,630,656,660,675,680,684,688,696]
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create_sequence_a018253(opts)

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OEIS Sequence A018253 - Divisors of 24.

From OEIS A018253:

Divisors of 24. (Formerly )

Sequence IDs: :a018253

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018253) |> Sequence.take!(8)
[1,2,3,4,6,8,12,24]
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create_sequence_a018256(opts)

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OEIS Sequence A018256 - Divisors of 36.

From OEIS A018256:

Divisors of 36. (Formerly )

Sequence IDs: :a018256

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018256) |> Sequence.take!(9)
[1,2,3,4,6,9,12,18,36]
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create_sequence_a018261(opts)

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OEIS Sequence A018261 - Divisors of 48.

From OEIS A018261:

Divisors of 48. (Formerly )

Sequence IDs: :a018261

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018261) |> Sequence.take!(10)
[1,2,3,4,6,8,12,16,24,48]
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create_sequence_a018266(opts)

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OEIS Sequence A018266 - Divisors of 60.

From OEIS A018266:

Divisors of 60. (Formerly )

Sequence IDs: :a018266

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018266) |> Sequence.take!(12)
[1,2,3,4,5,6,10,12,15,20,30,60]
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create_sequence_a018293(opts)

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OEIS Sequence A018293 - Divisors of 120.

From OEIS A018293:

Divisors of 120. (Formerly )

Sequence IDs: :a018293

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018293) |> Sequence.take!(16)
[1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120]
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create_sequence_a018321(opts)

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OEIS Sequence A018321 - Divisors of 180.

From OEIS A018321:

Divisors of 180. (Formerly )

Sequence IDs: :a018321

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018321) |> Sequence.take!(18)
[1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180]
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create_sequence_a018350(opts)

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OEIS Sequence A018350 - Divisors of 240.

From OEIS A018350:

Divisors of 240. (Formerly )

Sequence IDs: :a018350

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018350) |> Sequence.take!(20)
[1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240]
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create_sequence_a018412(opts)

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OEIS Sequence A018412 - Divisors of 360.

From OEIS A018412:

Divisors of 360. (Formerly )

Sequence IDs: :a018412

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018412) |> Sequence.take!(24)
[1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360]
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create_sequence_a018609(opts)

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OEIS Sequence A018609 - Divisors of 720.

From OEIS A018609:

Divisors of 720. (Formerly )

Sequence IDs: :a018609

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018609) |> Sequence.take!(30)
[1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720]
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create_sequence_a018676(opts)

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OEIS Sequence A018676 - Divisors of 840.

From OEIS A018676:

Divisors of 840. (Formerly )

Sequence IDs: :a018676

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a018676) |> Sequence.take!(32)
[1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840]
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create_sequence_a030513(opts)

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OEIS Sequence A030513 - Numbers with 4 divisors.

From OEIS A030513:

Numbers with 4 divisors. (Formerly )

Sequence IDs: :a030513

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a030513) |> Sequence.take!(58)
[6,8,10,14,15,21,22,26,27,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,82,85,86,87,91,93,94,95,106,111,115,118,119,122,123,125,129,133,134,141,142,143,145,146,155,158,159,161,166,177,178,183,185,187]
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create_sequence_a030515(opts)

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OEIS Sequence A030515 - Numbers with exactly 6 divisors.

From OEIS A030515:

Numbers with exactly 6 divisors.

Sequence IDs: :a030515

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a030515) |> Sequence.take!(52)
[12,18,20,28,32,44,45,50,52,63,68,75,76,92,98,99,116,117,124,147,148,153,164,171,172,175,188,207,212,236,242,243,244,245,261,268,275,279,284,292,316,325,332,333,338,356,363,369,387,388,404,412]
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create_sequence_a033273(opts)

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OEIS Sequence A033273 - Number of nonprime divisors of n.

From OEIS A033273:

Number of nonprime divisors of n.

Sequence IDs: :a033273

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a033273) |> Sequence.take!(104)
[1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,4,1,4,1,4,2,2,1,6,2,2,3,4,1,5,1,5,2,2,2,7,1,2,2,6,1,5,1,4,4,2,1,8,2,4,2,4,1,6,2,6,2,2,1,9,1,2,4,6,2,5,1,4,2,5,1,10,1,2,4,4,2,5,1,8,4,2,1,9,2,2,2,6,1,9,2,4,2,2,2,10,1,4,4,7,1,5,1,6]
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create_sequence_a033942(opts)

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OEIS Sequence A033942 - At least 3 prime factors (counted with multiplicity).

From OEIS A033942:

At least 3 prime factors (counted with multiplicity).

Sequence IDs: :a033942

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a033942) |> Sequence.take!(61)
[8,12,16,18,20,24,27,28,30,32,36,40,42,44,45,48,50,52,54,56,60,63,64,66,68,70,72,75,76,78,80,81,84,88,90,92,96,98,99,100,102,104,105,108,110,112,114,116,117,120,124,125,126,128,130,132,135,136,138,140,144]
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create_sequence_a033987(opts)

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OEIS Sequence A033987 - Numbers that are divisible by at least 4 primes (counted with multiplicity).

From OEIS A033987:

Numbers that are divisible by at least 4 primes (counted with multiplicity).

Sequence IDs: :a033987

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a033987) |> Sequence.take!(55)
[16,24,32,36,40,48,54,56,60,64,72,80,81,84,88,90,96,100,104,108,112,120,126,128,132,135,136,140,144,150,152,156,160,162,168,176,180,184,189,192,196,198,200,204,208,210,216,220,224,225,228,232,234,240,243]
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create_sequence_a033992(opts)

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OEIS Sequence A033992 - Numbers that are divisible by exactly three different primes.

From OEIS A033992:

Numbers that are divisible by exactly three different primes.

Sequence IDs: :a033992

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a033992) |> Sequence.take!(53)
[30,42,60,66,70,78,84,90,102,105,110,114,120,126,130,132,138,140,150,154,156,165,168,170,174,180,182,186,190,195,198,204,220,222,228,230,231,234,238,240,246,252,255,258,260,264,266,270,273,276,280,282,285]
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create_sequence_a033993(opts)

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OEIS Sequence A033993 - Numbers that are divisible by exactly four different primes.

From OEIS A033993:

Numbers that are divisible by exactly four different primes. (Formerly )

Sequence IDs: :a033993

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a033993) |> Sequence.take!(46)
[210,330,390,420,462,510,546,570,630,660,690,714,770,780,798,840,858,870,910,924,930,966,990,1020,1050,1092,1110,1122,1140,1155,1170,1190,1218,1230,1254,1260,1290,1302,1320,1326,1330,1365,1380,1386,1410,1428]
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create_sequence_a036537(opts)

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OEIS Sequence A036537 - Numbers whose number of divisors is a power of 2.

From OEIS A036537:

Numbers whose number of divisors is a power of 2. (Formerly )

Sequence IDs: :a036537

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a036537) |> Sequence.take!(70)
[1,2,3,5,6,7,8,10,11,13,14,15,17,19,21,22,23,24,26,27,29,30,31,33,34,35,37,38,39,40,41,42,43,46,47,51,53,54,55,56,57,58,59,61,62,65,66,67,69,70,71,73,74,77,78,79,82,83,85,86,87,88,89,91,93,94,95,97,101,102]
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create_sequence_a037143(opts)

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OEIS Sequence A037143 - Numbers with at most 2 prime factors (counted with multiplicity).

From OEIS A037143:

Numbers with at most 2 prime factors (counted with multiplicity).

Sequence IDs: :a037143

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a037143) |> Sequence.take!(69)
[1,2,3,4,5,6,7,9,10,11,13,14,15,17,19,21,22,23,25,26,29,31,33,34,35,37,38,39,41,43,46,47,49,51,53,55,57,58,59,61,62,65,67,69,71,73,74,77,79,82,83,85,86,87,89,91,93,94,95,97,101,103,106,107,109,111,113,115,118]
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create_sequence_a038109(opts)

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OEIS Sequence A038109 - Divisible exactly by the square of a prime.

From OEIS A038109:

Divisible exactly by the square of a prime.

Sequence IDs: :a038109

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a038109) |> Sequence.take!(58)
[4,9,12,18,20,25,28,36,44,45,49,50,52,60,63,68,72,75,76,84,90,92,98,99,100,108,116,117,121,124,126,132,140,144,147,148,150,153,156,164,169,171,172,175,180,188,196,198,200,204,207,212,220,225,228,234,236,242]
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create_sequence_a039956(opts)

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OEIS Sequence A039956 - Even squarefree numbers.

From OEIS A039956:

Even squarefree numbers. (Formerly )

Sequence IDs: :a039956

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a039956) |> Sequence.take!(54)
[2,6,10,14,22,26,30,34,38,42,46,58,62,66,70,74,78,82,86,94,102,106,110,114,118,122,130,134,138,142,146,154,158,166,170,174,178,182,186,190,194,202,206,210,214,218,222,226,230,238,246,254,258,262]
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create_sequence_a046099(opts)

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OEIS Sequence A046099 - Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709.

From OEIS A046099:

Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709. (Formerly )

Sequence IDs: :a046099

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046099) |> Sequence.take!(55)
[8,16,24,27,32,40,48,54,56,64,72,80,81,88,96,104,108,112,120,125,128,135,136,144,152,160,162,168,176,184,189,192,200,208,216,224,232,240,243,248,250,256,264,270,272,280,288,296,297,304,312,320,324,328,336]
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create_sequence_a046306(opts)

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OEIS Sequence A046306 - Numbers that are divisible by exactly 6 primes with multiplicity.

From OEIS A046306:

Numbers that are divisible by exactly 6 primes with multiplicity.

Sequence IDs: :a046306

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046306) |> Sequence.take!(49)
[64,96,144,160,216,224,240,324,336,352,360,400,416,486,504,528,540,544,560,600,608,624,729,736,756,784,792,810,816,840,880,900,912,928,936,992,1000,1040,1104,1134,1176,1184,1188,1215,1224,1232,1260,1312,1320]
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create_sequence_a046308(opts)

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OEIS Sequence A046308 - Numbers that are divisible by exactly 7 primes counting multiplicity.

From OEIS A046308:

Numbers that are divisible by exactly 7 primes counting multiplicity. (Formerly )

Sequence IDs: :a046308

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046308) |> Sequence.take!(44)
[128,192,288,320,432,448,480,648,672,704,720,800,832,972,1008,1056,1080,1088,1120,1200,1216,1248,1458,1472,1512,1568,1584,1620,1632,1680,1760,1800,1824,1856,1872,1984,2000,2080,2187,2208,2268,2352,2368,2376]
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create_sequence_a046310(opts)

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OEIS Sequence A046310 - Numbers that are divisible by exactly 8 primes counting multiplicity.

From OEIS A046310:

Numbers that are divisible by exactly 8 primes counting multiplicity.

Sequence IDs: :a046310

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046310) |> Sequence.take!(43)
[256,384,576,640,864,896,960,1296,1344,1408,1440,1600,1664,1944,2016,2112,2160,2176,2240,2400,2432,2496,2916,2944,3024,3136,3168,3240,3264,3360,3520,3600,3648,3712,3744,3968,4000,4160,4374,4416,4536,4704,4736]
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create_sequence_a046312(opts)

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OEIS Sequence A046312 - Numbers that are divisible by exactly 9 primes with multiplicity.

From OEIS A046312:

Numbers that are divisible by exactly 9 primes with multiplicity.

Sequence IDs: :a046312

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046312) |> Sequence.take!(42)
[512,768,1152,1280,1728,1792,1920,2592,2688,2816,2880,3200,3328,3888,4032,4224,4320,4352,4480,4800,4864,4992,5832,5888,6048,6272,6336,6480,6528,6720,7040,7200,7296,7424,7488,7936,8000,8320,8748,8832,9072,9408]
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create_sequence_a046314(opts)

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OEIS Sequence A046314 - Numbers that are divisible by exactly 10 primes with multiplicity.

From OEIS A046314:

Numbers that are divisible by exactly 10 primes with multiplicity.

Sequence IDs: :a046314

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046314) |> Sequence.take!(38)
[1024,1536,2304,2560,3456,3584,3840,5184,5376,5632,5760,6400,6656,7776,8064,8448,8640,8704,8960,9600,9728,9984,11664,11776,12096,12544,12672,12960,13056,13440,14080,14400,14592,14848,14976,15872,16000,16640]
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create_sequence_a046321(opts)

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OEIS Sequence A046321 - Odd numbers divisible by exactly 8 primes (counted with multiplicity).

From OEIS A046321:

Odd numbers divisible by exactly 8 primes (counted with multiplicity).

Sequence IDs: :a046321

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046321) |> Sequence.take!(33)
[6561,10935,15309,18225,24057,25515,28431,30375,35721,37179,40095,41553,42525,47385,50301,50625,56133,59535,61965,63423,66339,66825,67797,69255,70875,78975,80919,83349,83835,84375,86751,88209,89667]
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create_sequence_a046386(opts)

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OEIS Sequence A046386 - Products of four distinct primes.

From OEIS A046386:

Products of four distinct primes. (Formerly )

Sequence IDs: :a046386

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046386) |> Sequence.take!(45)
[210,330,390,462,510,546,570,690,714,770,798,858,870,910,930,966,1110,1122,1155,1190,1218,1230,1254,1290,1302,1326,1330,1365,1410,1430,1482,1518,1554,1590,1610,1722,1770,1785,1794,1806,1830,1870,1914,1938,1974]
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create_sequence_a046387(opts)

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OEIS Sequence A046387 - Products of 5 distinct primes.

From OEIS A046387:

Products of 5 distinct primes. (Formerly )

Sequence IDs: :a046387

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046387) |> Sequence.take!(38)
[2310,2730,3570,3990,4290,4830,5610,6006,6090,6270,6510,6630,7410,7590,7770,7854,8610,8778,8970,9030,9282,9570,9690,9870,10010,10230,10374,10626,11130,11310,11730,12090,12210,12390,12558,12810,13090,13110]
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create_sequence_a046660(opts)

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OEIS Sequence A046660 - Excess of n = number of prime divisors (with multiplicity) - number of prime divisors (without multiplicity).

From OEIS A046660:

Excess of n = number of prime divisors (with multiplicity) - number of prime divisors (without multiplicity).

Sequence IDs: :a046660

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046660) |> Sequence.take!(111)
[0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,3,0,1,0,1,0,0,0,2,1,0,2,1,0,0,0,4,0,0,0,2,0,0,0,2,0,0,0,1,1,0,0,3,1,1,0,1,0,2,0,2,0,0,0,1,0,0,1,5,0,0,0,1,0,0,0,3,0,0,1,1,0,0,0,3,3,0,0,1,0,0,0,2,0,1,0,1,0,0,0,4,0,1,1,2,0,0,0,2,0,0,0,3,0,0,0]
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create_sequence_a046758(opts)

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OEIS Sequence A046758 - Equidigital numbers.

From OEIS A046758:

Equidigital numbers. (Formerly )

Sequence IDs: :a046758

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046758) |> Sequence.take!(61)
[1,2,3,5,7,10,11,13,14,15,16,17,19,21,23,25,27,29,31,32,35,37,41,43,47,49,53,59,61,64,67,71,73,79,81,83,89,97,101,103,105,106,107,109,111,112,113,115,118,119,121,122,123,127,129,131,133,134,135,137,139]
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create_sequence_a046759(opts)

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OEIS Sequence A046759 - Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n).

From OEIS A046759:

Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n). (Formerly )

Sequence IDs: :a046759

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046759) |> Sequence.take!(41)
[125,128,243,256,343,512,625,729,1024,1029,1215,1250,1280,1331,1369,1458,1536,1681,1701,1715,1792,1849,1875,2048,2187,2197,2209,2401,2560,2809,3125,3481,3584,3645,3721,4096,4374,4375,4489,4802,4913]
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create_sequence_a046760(opts)

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OEIS Sequence A046760 - Wasteful numbers.

From OEIS A046760:

Wasteful numbers. (Formerly )

Sequence IDs: :a046760

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a046760) |> Sequence.take!(67)
[4,6,8,9,12,18,20,22,24,26,28,30,33,34,36,38,39,40,42,44,45,46,48,50,51,52,54,55,56,57,58,60,62,63,65,66,68,69,70,72,74,75,76,77,78,80,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100,102,104,108,110,114]
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create_sequence_a048272(opts)

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OEIS Sequence A048272 - Number of odd divisors of n minus number of even divisors of n.

From OEIS A048272:

Number of odd divisors of n minus number of even divisors of n.

Sequence IDs: :a048272

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a048272) |> Sequence.take!(93)
[1,0,2,-1,2,0,2,-2,3,0,2,-2,2,0,4,-3,2,0,2,-2,4,0,2,-4,3,0,4,-2,2,0,2,-4,4,0,4,-3,2,0,4,-4,2,0,2,-2,6,0,2,-6,3,0,4,-2,2,0,4,-4,4,0,2,-4,2,0,6,-5,4,0,2,-2,4,0,2,-6,2,0,6,-2,4,0,2,-6,5,0,2,-4,4,0,4,-4,2,0,4,-2,4]
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create_sequence_a051037(opts)

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OEIS Sequence A051037 - 5-smooth Numbers

From OEIS A051037:

5-smooth numbers, i.e., numbers whose prime divisors are all <= 5

Sequence IDs: :a051037

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a051037) |> Sequence.drop(20) |> Sequence.take!(20)
[40, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125, 128, 135, 144]
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create_sequence_a051038(opts)

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OEIS Sequence A051038 - 11-smooth Numbers

From OEIS A051038:

11-smooth numbers: numbers whose prime divisors are all <= 11.

Sequence IDs: :a051038

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a051038) |> Sequence.drop(20) |> Sequence.take!(20)
[25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63]
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create_sequence_a051270(opts)

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OEIS Sequence A051270 - Numbers that are divisible by exactly 5 different primes.

From OEIS A051270:

Numbers that are divisible by exactly 5 different primes.

Sequence IDs: :a051270

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a051270) |> Sequence.take!(40)
[2310,2730,3570,3990,4290,4620,4830,5460,5610,6006,6090,6270,6510,6630,6930,7140,7410,7590,7770,7854,7980,8190,8580,8610,8778,8970,9030,9240,9282,9570,9660,9690,9870,10010,10230,10374,10626,10710,10920,11130]
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create_sequence_a052486(opts)

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OEIS Sequence A052486 - Achilles numbers - powerful but imperfect

From OEIS A052486:

Achilles numbers - powerful but imperfect: if n = Product(p_i^e_i) then all e_i > 1 (i.e., powerful), but the highest common factor of the e_i is 1, i.e., not a perfect power.

Sequence IDs: :a052486

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a052486) |> Sequence.take!(20)
[72, 108, 200, 288, 392, 432, 500, 648, 675, 800, 864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1800]
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create_sequence_a056911(opts)

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OEIS Sequence A056911 - Odd squarefree numbers.

From OEIS A056911:

Odd squarefree numbers. (Formerly )

Sequence IDs: :a056911

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a056911) |> Sequence.take!(62)
[1,3,5,7,11,13,15,17,19,21,23,29,31,33,35,37,39,41,43,47,51,53,55,57,59,61,65,67,69,71,73,77,79,83,85,87,89,91,93,95,97,101,103,105,107,109,111,113,115,119,123,127,129,131,133,137,139,141,143,145,149,151]
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create_sequence_a059269(opts)

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OEIS Sequence A059269 - Numbers n for which the number of divisors, tau(n), is divisible by 3.

From OEIS A059269:

Numbers n for which the number of divisors, tau(n), is divisible by 3. (Formerly )

Sequence IDs: :a059269

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a059269) |> Sequence.take!(59)
[4,9,12,18,20,25,28,32,36,44,45,49,50,52,60,63,68,72,75,76,84,90,92,96,98,99,100,108,116,117,121,124,126,132,140,144,147,148,150,153,156,160,164,169,171,172,175,180,188,196,198,200,204,207,212,220,224,225,228]
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create_sequence_a059376(opts)

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OEIS Sequence A059376 - Jordan function J_3(n).

From OEIS A059376:

Jordan function J_3(n). (Formerly )

Sequence IDs: :a059376

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a059376) |> Sequence.take!(39)
[1,7,26,56,124,182,342,448,702,868,1330,1456,2196,2394,3224,3584,4912,4914,6858,6944,8892,9310,12166,11648,15500,15372,18954,19152,24388,22568,29790,28672,34580,34384,42408,39312,50652,48006,57096]
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create_sequence_a059377(opts)

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OEIS Sequence A059377 - Jordan function J_4(n).

From OEIS A059377:

Jordan function J_4(n). (Formerly )

Sequence IDs: :a059377

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a059377) |> Sequence.take!(33)
[1,15,80,240,624,1200,2400,3840,6480,9360,14640,19200,28560,36000,49920,61440,83520,97200,130320,149760,192000,219600,279840,307200,390000,428400,524880,576000,707280,748800,923520,983040,1171200]
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create_sequence_a059378(opts)

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OEIS Sequence A059378 - Jordan function J_5(n).

From OEIS A059378:

Jordan function J_5(n). (Formerly )

Sequence IDs: :a059378

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a059378) |> Sequence.take!(29)
[1,31,242,992,3124,7502,16806,31744,58806,96844,161050,240064,371292,520986,756008,1015808,1419856,1822986,2476098,3099008,4067052,4992550,6436342,7682048,9762500,11510052,14289858,16671552,20511148]
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create_sequence_a065958(opts)

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OEIS Sequence A065958 - a(n) = n^2*Product_{distinct primes p dividing n} (1+1/p^2).

From OEIS A065958:

a(n) = n^2*Product_{distinct primes p dividing n} (1+1/p^2).

Sequence IDs: :a065958

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a065958) |> Sequence.take!(47)
[1,5,10,20,26,50,50,80,90,130,122,200,170,250,260,320,290,450,362,520,500,610,530,800,650,850,810,1000,842,1300,962,1280,1220,1450,1300,1800,1370,1810,1700,2080,1682,2500,1850,2440,2340,2650,2210]
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create_sequence_a065959(opts)

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OEIS Sequence A065959 - a(n) = n^3*Product_{distinct primes p dividing n} (1+1/p^3).

From OEIS A065959:

a(n) = n^3*Product_{distinct primes p dividing n} (1+1/p^3). (Formerly )

Sequence IDs: :a065959

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a065959) |> Sequence.take!(39)
[1,9,28,72,126,252,344,576,756,1134,1332,2016,2198,3096,3528,4608,4914,6804,6860,9072,9632,11988,12168,16128,15750,19782,20412,24768,24390,31752,29792,36864,37296,44226,43344,54432,50654,61740,61544]
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create_sequence_a065960(opts)

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OEIS Sequence A065960 - a(n) = n^4*Product_{distinct primes p dividing n} (1+1/p^4).

From OEIS A065960:

a(n) = n^4*Product_{distinct primes p dividing n} (1+1/p^4).

Sequence IDs: :a065960

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a065960) |> Sequence.take!(33)
[1,17,82,272,626,1394,2402,4352,6642,10642,14642,22304,28562,40834,51332,69632,83522,112914,130322,170272,196964,248914,279842,356864,391250,485554,538002,653344,707282,872644,923522,1114112,1200644]
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create_sequence_a067259(opts)

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OEIS Sequence A067259 - Cubefree numbers which are not squarefree.

From OEIS A067259:

Cubefree numbers which are not squarefree.

Sequence IDs: :a067259

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a067259) |> Sequence.take!(51)
[4,9,12,18,20,25,28,36,44,45,49,50,52,60,63,68,75,76,84,90,92,98,99,100,116,117,121,124,126,132,140,147,148,150,153,156,164,169,171,172,175,180,188,196,198,204,207,212,220,225,228]
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create_sequence_a067885(opts)

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OEIS Sequence A067885 - Product of 6 distinct primes.

From OEIS A067885:

Product of 6 distinct primes. (Formerly )

Sequence IDs: :a067885

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a067885) |> Sequence.take!(32)
[30030,39270,43890,46410,51870,53130,62790,66990,67830,71610,72930,79170,81510,82110,84630,85470,91770,94710,98670,99330,101010,102102,103530,106590,108570,110670,111930,114114,115710,117390,122430,123690]
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create_sequence_a069091(opts)

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OEIS Sequence A069091 - Jordan function J_6(n).

From OEIS A069091:

Jordan function J_6(n).

Sequence IDs: :a069091

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a069091) |> Sequence.take!(27)
[1,63,728,4032,15624,45864,117648,258048,530712,984312,1771560,2935296,4826808,7411824,11374272,16515072,24137568,33434856,47045880,62995968,85647744,111608280,148035888,187858944,244125000,304088904,386889048]
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create_sequence_a069092(opts)

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OEIS Sequence A069092 - Jordan function J_7(n).

From OEIS A069092:

Jordan function J_7(n).

Sequence IDs: :a069092

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a069092) |> Sequence.take!(24)
[1,127,2186,16256,78124,277622,823542,2080768,4780782,9921748,19487170,35535616,62748516,104589834,170779064,266338304,410338672,607159314,893871738,1269983744,1800262812,2474870590,3404825446,4548558848]
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create_sequence_a069093(opts)

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OEIS Sequence A069093 - Jordan function J_8(n).

From OEIS A069093:

Jordan function J_8(n).

Sequence IDs: :a069093

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a069093) |> Sequence.take!(21)
[1,255,6560,65280,390624,1672800,5764800,16711680,43040160,99609120,214358880,428236800,815730720,1470024000,2562493440,4278190080,6975757440,10975240800,16983563040,25499934720,37817088000]
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create_sequence_a069094(opts)

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OEIS Sequence A069094 - Jordan function J_9(n).

From OEIS A069094:

Jordan function J_9(n).

Sequence IDs: :a069094

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a069094) |> Sequence.take!(20)
[1,511,19682,261632,1953124,10057502,40353606,133955584,387400806,998046364,2357947690,5149441024,10604499372,20620692666,38441386568,68585259008,118587876496,197961811866,322687697778,510999738368]
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create_sequence_a069095(opts)

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OEIS Sequence A069095 - Jordan function J_10(n).

From OEIS A069095:

Jordan function J_10(n).

Sequence IDs: :a069095

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a069095) |> Sequence.take!(19)
[1,1023,59048,1047552,9765624,60406104,282475248,1072693248,3486725352,9990233352,25937424600,61855850496,137858491848,288972178704,576640565952,1098437885952,2015993900448,3566920035096,6131066257800]
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create_sequence_a069272(opts)

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OEIS Sequence A069272 - 11-almost primes (generalization of semiprimes).

From OEIS A069272:

11-almost primes (generalization of semiprimes).

Sequence IDs: :a069272

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069272) |> Sequence.take!(34)
[2048,3072,4608,5120,6912,7168,7680,10368,10752,11264,11520,12800,13312,15552,16128,16896,17280,17408,17920,19200,19456,19968,23328,23552,24192,25088,25344,25920,26112,26880,28160,28800,29184,29696]
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create_sequence_a069273(opts)

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OEIS Sequence A069273 - 12-almost primes (generalization of semiprimes).

From OEIS A069273:

12-almost primes (generalization of semiprimes).

Sequence IDs: :a069273

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069273) |> Sequence.take!(34)
[4096,6144,9216,10240,13824,14336,15360,20736,21504,22528,23040,25600,26624,31104,32256,33792,34560,34816,35840,38400,38912,39936,46656,47104,48384,50176,50688,51840,52224,53760,56320,57600,58368,59392]
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create_sequence_a069274(opts)

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OEIS Sequence A069274 - 13-almost primes (generalization of semiprimes).

From OEIS A069274:

13-almost primes (generalization of semiprimes).

Sequence IDs: :a069274

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069274) |> Sequence.take!(32)
[8192,12288,18432,20480,27648,28672,30720,41472,43008,45056,46080,51200,53248,62208,64512,67584,69120,69632,71680,76800,77824,79872,93312,94208,96768,100352,101376,103680,104448,107520,112640,115200]
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create_sequence_a069275(opts)

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OEIS Sequence A069275 - 14-almost primes (generalization of semiprimes).

From OEIS A069275:

14-almost primes (generalization of semiprimes).

Sequence IDs: :a069275

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069275) |> Sequence.take!(5)
[16384,24576,36864,40960,55296]
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create_sequence_a069276(opts)

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OEIS Sequence A069276 - 15-almost primes (generalization of semiprimes).

From OEIS A069276:

15-almost primes (generalization of semiprimes).

Sequence IDs: :a069276

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069276) |> Sequence.take!(5)
[32768,49152,73728,81920,110592]
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create_sequence_a069277(opts)

View Source

OEIS Sequence A069277 - 16-almost primes (generalization of semiprimes).

From OEIS A069277:

16-almost primes (generalization of semiprimes).

Sequence IDs: :a069277

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069277) |> Sequence.take!(5)
[65536,98304,147456,163840,221184]
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create_sequence_a069278(opts)

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OEIS Sequence A069278 - 17-almost primes (generalization of semiprimes).

From OEIS A069278:

17-almost primes (generalization of semiprimes).

Sequence IDs: :a069278

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069278) |> Sequence.take!(3)
[131072,196608,294912]
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create_sequence_a069279(opts)

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OEIS Sequence A069279 - Products of exactly 18 primes (generalization of semiprimes).

From OEIS A069279:

Products of exactly 18 primes (generalization of semiprimes).

Sequence IDs: :a069279

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069279) |> Sequence.take!(2)
[262144,393216]
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create_sequence_a069280(opts)

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OEIS Sequence A069280 - 19-almost primes (generalization of semiprimes).

From OEIS A069280:

19-almost primes (generalization of semiprimes).

Sequence IDs: :a069280

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069280) |> Sequence.take!(1)
[524288]
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create_sequence_a069281(opts)

View Source

OEIS Sequence A069281 - 20-almost primes (generalization of semiprimes).

From OEIS A069281:

20-almost primes (generalization of semiprimes).

Sequence IDs: :a069281

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a069281) |> Sequence.take!(1)
[1048576]
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create_sequence_a074969(opts)

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OEIS Sequence A074969 - Numbers with six distinct prime divisors.

From OEIS A074969:

Numbers with six distinct prime divisors.

Sequence IDs: :a074969

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a074969) |> Sequence.take!(32)
[30030,39270,43890,46410,51870,53130,60060,62790,66990,67830,71610,72930,78540,79170,81510,82110,84630,85470,87780,90090,91770,92820,94710,98670,99330,101010,102102,103530,103740,106260,106590,108570]
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create_sequence_a076479(opts)

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OEIS Sequence A076479 - a(n) = mu(rad(n)), where mu is the Moebius-function

From OEIS A076479:

a(n) = mu(rad(n)), where mu is the Moebius-function (A008683) and rad is the radical or squarefree kernel (A007947).

Sequence IDs: :a076479

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a076479) |> Sequence.take!(87)
[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]
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create_sequence_a080197(opts)

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OEIS Sequence A080197 - 13-smooth Numbers

From OEIS A080197:

13-smooth numbers: numbers whose prime divisors are all <= 13.

Sequence IDs: :a080197

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a080197) |> Sequence.drop(20) |> Sequence.take!(20)
[24, 25, 26, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 52, 54]
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create_sequence_a080681(opts)

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OEIS Sequence A080681 - 17-smooth Numbers

From OEIS A080681:

17-smooth numbers: numbers whose prime divisors are all <= 17.

Sequence IDs: :a080681

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a080681) |> Sequence.drop(20) |> Sequence.take!(20)
[22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50]
Link to this function

create_sequence_a080682(opts)

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OEIS Sequence A080682 - 19-smooth Numbers

From OEIS A080682:

19-smooth numbers: numbers whose prime divisors are all <= 19.

Sequence IDs: :a080682

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a080682) |> Sequence.drop(20) |> Sequence.take!(20)
[21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 48]
Link to this function

create_sequence_a080683(opts)

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OEIS Sequence A080683 - 23-smooth Numbers

From OEIS A080683:

23-smooth numbers: numbers whose prime divisors are all <= 23.

Sequence IDs: :a080683

Finite: False

Offset: 1

Example 

iex> Sequence.create(Sequence.OEIS.Factors, :a080683) |> Sequence.drop(20) |> Sequence.take!(20)
[21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45]
Link to this function

create_sequence_a117805(opts)

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OEIS Sequence A117805 - Start with 3. Square the previous term and subtract it.

From OEIS A117805:

Start with 3. Square the previous term and subtract it.

Sequence IDs: :a117805

Finite: False

Offset: 0

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a117805) |> Sequence.take!(9)
[3,6,30,870,756030,571580604870,326704387862983487112030,106735757048926752040856495274871386126283608870,11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068030]
Link to this function

create_sequence_a123321(opts)

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OEIS Sequence A123321 - Products of 7 distinct primes (squarefree 7-almost primes).

From OEIS A123321:

Products of 7 distinct primes (squarefree 7-almost primes).

Sequence IDs: :a123321

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a123321) |> Sequence.take!(2)
[510510,570570]
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create_sequence_a123322(opts)

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OEIS Sequence A123322 - Products of 8 distinct primes (squarefree 8-almost primes).

From OEIS A123322:

Products of 8 distinct primes (squarefree 8-almost primes).

Sequence IDs: :a123322

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a123322) |> Sequence.take!(1)
[9699690]
Link to this function

create_sequence_a130897(opts)

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OEIS Sequence A130897 - Numbers that are not exponentially squarefree.

From OEIS A130897:

Numbers that are not exponentially squarefree.

Sequence IDs: :a130897

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a130897) |> Sequence.take!(43)
[16,48,80,81,112,144,162,176,208,240,256,272,304,324,336,368,400,405,432,464,496,512,528,560,567,592,624,625,648,656,688,720,752,768,784,810,816,848,880,891,912,944,976]
Link to this function

create_sequence_a160889(opts)

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OEIS Sequence A160889 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4.

From OEIS A160889:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4.

Sequence IDs: :a160889

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160889) |> Sequence.take!(49)
[1,7,13,28,31,91,57,112,117,217,133,364,183,399,403,448,307,819,381,868,741,931,553,1456,775,1281,1053,1596,871,2821,993,1792,1729,2149,1767,3276,1407,2667,2379,3472,1723,5187,1893,3724,3627,3871,2257,5824,2793]
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create_sequence_a160891(opts)

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OEIS Sequence A160891 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 5.

From OEIS A160891:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 5.

Sequence IDs: :a160891

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160891) |> Sequence.take!(39)
[1,15,40,120,156,600,400,960,1080,2340,1464,4800,2380,6000,6240,7680,5220,16200,7240,18720,16000,21960,12720,38400,19500,35700,29160,48000,25260,93600,30784,61440,58560,78300,62400,129600,52060,108600,95200]
Link to this function

create_sequence_a160893(opts)

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OEIS Sequence A160893 - a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n).

From OEIS A160893:

a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n).

Sequence IDs: :a160893

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160893) |> Sequence.take!(33)
[1,31,121,496,781,3751,2801,7936,9801,24211,16105,60016,30941,86831,94501,126976,88741,303831,137561,387376,338921,499255,292561,960256,488125,959171,793881,1389296,732541,2929531,954305,2031616,1948705]
Link to this function

create_sequence_a160895(opts)

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OEIS Sequence A160895 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7.

From OEIS A160895:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7. (Formerly )

Sequence IDs: :a160895

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160895) |> Sequence.take!(30)
[1,63,364,2016,3906,22932,19608,64512,88452,246078,177156,733824,402234,1235304,1421784,2064384,1508598,5572476,2613660,7874496,7137312,11160828,6728904,23482368,12206250,25340742,21493836,39529728,21243690,89572392]
Link to this function

create_sequence_a160897(opts)

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OEIS Sequence A160897 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8.

From OEIS A160897:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8.

Sequence IDs: :a160897

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160897) |> Sequence.take!(26)
[1,127,1093,8128,19531,138811,137257,520192,796797,2480437,1948717,8883904,5229043,17431639,21347383,33292288,25646167,101193219,49659541,158747968,150021901,247487059,154764793,568569856,305171875,664088461]
Link to this function

create_sequence_a160908(opts)

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OEIS Sequence A160908 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 9.

From OEIS A160908:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 9.

Sequence IDs: :a160908

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160908) |> Sequence.take!(24)
[1,255,3280,32640,97656,836400,960800,4177920,7173360,24902280,21435888,107059200,67977560,245004000,320311680,534773760,435984840,1829206800,943531280,3187491840,3151424000,5466151440,3559590240,13703577600]
Link to this function

create_sequence_a160953(opts)

View Source

OEIS Sequence A160953 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10.

From OEIS A160953:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10.

Sequence IDs: :a160953

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160953) |> Sequence.take!(21)
[1,511,9841,130816,488281,5028751,6725601,33488896,64566801,249511591,235794769,1287360256,883708281,3436782111,4805173321,8573157376,7411742281,32993635311,17927094321,63874967296,66186639441]
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create_sequence_a160957(opts)

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OEIS Sequence A160957 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11.

From OEIS A160957:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11.

Sequence IDs: :a160957

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160957) |> Sequence.take!(20)
[1,1023,29524,523776,2441406,30203052,47079208,268173312,581120892,2497558338,2593742460,15463962624,11488207654,48162029784,72080070744,137304735744,125999618778,594486672516,340614792100,1278749869056]
Link to this function

create_sequence_a160960(opts)

View Source

OEIS Sequence A160960 - a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 12.

From OEIS A160960:

a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 12.

Sequence IDs: :a160960

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a160960) |> Sequence.take!(18)
[1,2047,88573,2096128,12207031,181308931,329554457,2146435072,5230147077,24987792457,28531167061,185660345344,149346699503,674597973479,1081213356763,2197949513728,2141993519227,10706111066619]
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create_sequence_a162643(opts)

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OEIS Sequence A162643 - Numbers such that their number of divisors is not a power of 2.

From OEIS A162643:

Numbers such that their number of divisors is not a power of 2.

Sequence IDs: :a162643

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a162643) |> Sequence.take!(60)
[4,9,12,16,18,20,25,28,32,36,44,45,48,49,50,52,60,63,64,68,72,75,76,80,81,84,90,92,96,98,99,100,108,112,116,117,121,124,126,132,140,144,147,148,150,153,156,160,162,164,169,171,172,175,176,180,188,192,196,198]
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create_sequence_a165412(opts)

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OEIS Sequence A165412 - Divisors of 2520.

From OEIS A165412:

Divisors of 2520. (Formerly )

Sequence IDs: :a165412

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a165412) |> Sequence.take!(48)
[1,2,3,4,5,6,7,8,9,10,12,14,15,18,20,21,24,28,30,35,36,40,42,45,56,60,63,70,72,84,90,105,120,126,140,168,180,210,252,280,315,360,420,504,630,840,1260,2520]
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create_sequence_a178858(opts)

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OEIS Sequence A178858 - Divisors of 5040.

From OEIS A178858:

Divisors of 5040. (Formerly )

Sequence IDs: :a178858

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178858) |> Sequence.take!(60)
[1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,28,30,35,36,40,42,45,48,56,60,63,70,72,80,84,90,105,112,120,126,140,144,168,180,210,240,252,280,315,336,360,420,504,560,630,720,840,1008,1260,1680,2520,5040]
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create_sequence_a178859(opts)

View Source

OEIS Sequence A178859 - Divisors of 7560.

From OEIS A178859:

Divisors of 7560. (Formerly )

Sequence IDs: :a178859

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178859) |> Sequence.take!(61)
[1,2,3,4,5,6,7,8,9,10,12,14,15,18,20,21,24,27,28,30,35,36,40,42,45,54,56,60,63,70,72,84,90,105,108,120,126,135,140,168,180,189,210,216,252,270,280,315,360,378,420,504,540,630,756,840,945,1080,1260,1512,1890]
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create_sequence_a178860(opts)

View Source

OEIS Sequence A178860 - Divisors of 10080.

From OEIS A178860:

Divisors of 10080. (Formerly )

Sequence IDs: :a178860

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178860) |> Sequence.take!(63)
[1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,28,30,32,35,36,40,42,45,48,56,60,63,70,72,80,84,90,96,105,112,120,126,140,144,160,168,180,210,224,240,252,280,288,315,336,360,420,480,504,560,630,672,720,840,1008]
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create_sequence_a178861(opts)

View Source

OEIS Sequence A178861 - Divisors of 15120.

From OEIS A178861:

Divisors of 15120. (Formerly )

Sequence IDs: :a178861

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178861) |> Sequence.take!(63)
[1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,27,28,30,35,36,40,42,45,48,54,56,60,63,70,72,80,84,90,105,108,112,120,126,135,140,144,168,180,189,210,216,240,252,270,280,315,336,360,378,420,432,504,540,560,630]
Link to this function

create_sequence_a178862(opts)

View Source

OEIS Sequence A178862 - Divisors of 20160.

From OEIS A178862:

Divisors of 20160. (Formerly )

Sequence IDs: :a178862

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178862) |> Sequence.take!(63)
[1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,28,30,32,35,36,40,42,45,48,56,60,63,64,70,72,80,84,90,96,105,112,120,126,140,144,160,168,180,192,210,224,240,252,280,288,315,320,336,360,420,448,480,504,560,576]
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create_sequence_a178863(opts)

View Source

OEIS Sequence A178863 - Divisors of 25200.

From OEIS A178863:

Divisors of 25200. (Formerly )

Sequence IDs: :a178863

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178863) |> Sequence.take!(63)
[1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,25,28,30,35,36,40,42,45,48,50,56,60,63,70,72,75,80,84,90,100,105,112,120,126,140,144,150,168,175,180,200,210,225,240,252,280,300,315,336,350,360,400,420,450,504]
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create_sequence_a178864(opts)

View Source

OEIS Sequence A178864 - Divisors of 27720.

From OEIS A178864:

Divisors of 27720. (Formerly )

Sequence IDs: :a178864

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178864) |> Sequence.take!(64)
[1,2,3,4,5,6,7,8,9,10,11,12,14,15,18,20,21,22,24,28,30,33,35,36,40,42,44,45,55,56,60,63,66,70,72,77,84,88,90,99,105,110,120,126,132,140,154,165,168,180,198,210,220,231,252,264,280,308,315,330,360,385,396,420]
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create_sequence_a178877(opts)

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OEIS Sequence A178877 - Divisors of 1260.

From OEIS A178877:

Divisors of 1260. (Formerly )

Sequence IDs: :a178877

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178877) |> Sequence.take!(36)
[1,2,3,4,5,6,7,9,10,12,14,15,18,20,21,28,30,35,36,42,45,60,63,70,84,90,105,126,140,180,210,252,315,420,630,1260]
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create_sequence_a178878(opts)

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OEIS Sequence A178878 - Divisors of 1680.

From OEIS A178878:

Divisors of 1680. (Formerly )

Sequence IDs: :a178878

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a178878) |> Sequence.take!(40)
[1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,35,40,42,48,56,60,70,80,84,105,112,120,140,168,210,240,280,336,420,560,840,1680]
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create_sequence_a209061(opts)

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OEIS Sequence A209061 - Exponentially squarefree numbers.

From OEIS A209061:

Exponentially squarefree numbers.

Sequence IDs: :a209061

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a209061) |> Sequence.take!(67)
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69]
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create_sequence_a211337(opts)

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OEIS Sequence A211337 - Numbers n for which the number of divisors, tau(n), is congruent to 1 modulo 3.

From OEIS A211337:

Numbers n for which the number of divisors, tau(n), is congruent to 1 modulo 3.

Sequence IDs: :a211337

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a211337) |> Sequence.take!(59)
[1,6,8,10,14,15,21,22,26,27,33,34,35,38,39,46,48,51,55,57,58,62,64,65,69,74,77,80,82,85,86,87,91,93,94,95,106,111,112,115,118,119,120,122,123,125,129,133,134,141,142,143,145,146,155,158,159,161,162]
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create_sequence_a211338(opts)

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OEIS Sequence A211338 - Numbers n for which the number of divisors, tau(n), is congruent to 2 modulo 3.

From OEIS A211338:

Numbers n for which the number of divisors, tau(n), is congruent to 2 modulo 3.

Sequence IDs: :a211338

Finite: False

Offset: 1

Example 

iex> Sequence.create(Elixir.Chunky.Sequence.OEIS.Factors, :a211338) |> Sequence.take!(60)
[2,3,5,7,11,13,16,17,19,23,24,29,30,31,37,40,41,42,43,47,53,54,56,59,61,66,67,70,71,73,78,79,81,83,88,89,97,101,102,103,104,105,107,109,110,113,114,127,128,130,131,135,136,137,138,139,149,151,152,154]
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seq_a000037(idx, last)

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seq_a000977(idx, last)

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seq_a001414(idx)

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seq_a001597(idx, last)

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seq_a001694(idx, last)

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seq_a001826(idx)

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seq_a001842(idx)

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seq_a002473(idx, last)

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seq_a003586(idx, last)

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seq_a004709(idx, last)

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seq_a005361(idx)

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seq_a006881(idx, last)

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seq_a007018(idx, last)

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seq_a007304(idx, last)

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seq_a007412(idx, last)

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seq_a007434(idx)

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seq_a007774(idx, last)

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seq_a007947(idx)

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seq_a008966(idx)

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seq_a013929(idx, last)

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seq_a014612(idx, last)

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seq_a014613(idx, last)

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seq_a014614(idx, last)

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seq_a030513(idx, last)

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seq_a030515(idx, last)

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seq_a033273(idx)

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seq_a033942(idx, last)

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seq_a033987(idx, last)

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seq_a033992(idx, last)

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seq_a033993(idx, last)

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seq_a036537(idx, last)

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seq_a037143(idx, last)

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seq_a038109(idx, last)

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seq_a039956(idx, last)

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seq_a046099(idx, last)

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seq_a046306(idx, last)

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seq_a046308(idx, last)

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seq_a046310(idx, last)

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seq_a046312(idx, last)

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seq_a046314(idx, last)

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seq_a046321(idx, last)

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seq_a046386(idx, last)

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seq_a046387(idx, last)

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seq_a046660(idx)

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seq_a046758(idx, last)

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seq_a046759(idx, last)

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seq_a046760(idx, last)

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seq_a048272(idx)

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seq_a051037(idx, last)

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seq_a051038(idx, last)

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seq_a051270(idx, last)

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seq_a052486(idx, last)

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seq_a056911(idx, last)

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seq_a059269(idx, last)

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seq_a059376(idx)

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seq_a059377(idx)

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seq_a059378(idx)

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seq_a065958(idx)

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seq_a065959(idx)

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seq_a065960(idx)

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seq_a067259(idx, last)

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seq_a067885(idx, last)

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seq_a069091(idx)

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seq_a069092(idx)

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seq_a069093(idx)

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seq_a069094(idx)

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seq_a069095(idx)

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seq_a069272(idx, last)

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seq_a069273(idx, last)

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seq_a069274(idx, last)

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seq_a069275(idx, last)

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seq_a069276(idx, last)

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seq_a069277(idx, last)

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seq_a069278(idx, last)

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seq_a069279(idx, last)

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seq_a069280(idx, last)

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seq_a069281(idx, last)

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seq_a074969(idx, last)

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seq_a076479(idx)

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seq_a080197(idx, last)

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seq_a080681(idx, last)

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seq_a080682(idx, last)

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seq_a080683(idx, last)

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seq_a117805(idx, last)

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seq_a123321(idx, last)

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seq_a123322(idx, last)

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seq_a130897(idx, last)

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seq_a160889(idx)

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seq_a160891(idx)

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seq_a160893(idx)

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seq_a160895(idx)

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seq_a160897(idx)

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seq_a160908(idx)

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seq_a160953(idx)

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seq_a160957(idx)

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seq_a160960(idx)

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seq_a162643(idx, last)

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seq_a209061(idx, last)

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seq_a211337(idx, last)

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seq_a211338(idx, last)

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