chunky v0.12.0 Chunky.Sequence.OEIS.Sigma View Source
OEIS Sequences for Sigma values.
Some sigma sequences are in the Sequence.OEIS.Core module.
Available Sequences
- A001158 - Sum of cubes of divisors of N, simga-3(n) -
:a001158-create_sequence_a001158/1 - A001159 - sum of 4th powers of divisors of n, simga-4(n) -
a001159-create_sequence_a001159/1 - A001160 - sum of 5th powers of divisors of n, simga-5(n) -
a001160-create_sequence_a001160/1 - A002093 - Highly Abundant Numbers -
a002093-create_sequence_a002093/1 - A003601 - Arithmetic Numbers -
a003601-create_sequence_a003601/1 - A013954 - sum of 6th powers of divisors of n, simga-6(n) -
a013954-create_sequence_a013954/1 - A013955 - sum of 7th powers of divisors of n, simga-7(n) -
a013955-create_sequence_a013955/1 - A013956 - sum of 8th powers of divisors of n, simga-8(n) -
a013956-create_sequence_a013956/1 - A013957 - sum of 9th powers of divisors of n, simga-9(n) -
a013957-create_sequence_a013957/1 - A013958 - sum of 10th powers of divisors of n, simga-10(n) -
a013958-create_sequence_a013958/1 - A013959 - sum of 11th powers of divisors of n, simga-11(n) -
a013959-create_sequence_a013959/1 - A013960 - sum of 12th powers of divisors of n, simga-12(n) -
a013960-create_sequence_a013960/1 - A013961 - sum of 13th powers of divisors of n, simga-13(n) -
a013961-create_sequence_a013961/1 - A013962 - sum of 14th powers of divisors of n, simga-14(n) -
a013962-create_sequence_a013962/1 - A013963 - sum of 15th powers of divisors of n, simga-15(n) -
a013963-create_sequence_a013963/1 - A013964 - sum of 16th powers of divisors of n, simga-16(n) -
a013964-create_sequence_a013964/1 - A013965 - sum of 17th powers of divisors of n, simga-17(n) -
a013965-create_sequence_a013965/1 - A013966 - sum of 18th powers of divisors of n, simga-18(n) -
a013966-create_sequence_a013966/1 - A013967 - sum of 19th powers of divisors of n, simga-19(n) -
a013967-create_sequence_a013967/1 - A013968 - sum of 20th powers of divisors of n, simga-20(n) -
a013968-create_sequence_a013968/1
Link to this section Summary
Functions
OEIS Sequence A001158 - Sum of cubes of divisors of N, simga-3(n), 𝝈3(n).
OEIS Sequence A001159 - sum of 4th powers of divisors of n, simga-4(n), 𝝈4(n).
OEIS Sequence A001160 - sum of 5th powers of divisors of n, simga-5(n), 𝝈5(n).
OEIS Sequence A002093 - Highly Abundant Numbers
OEIS Sequence A003601 - Arithmetic Numbers
OEIS Sequence A013954 - sum of 6th powers of divisors of n, simga-6(n), 𝝈6(n).
OEIS Sequence A013955 - sum of 7th powers of divisors of n, simga-7(n), 𝝈7(n).
OEIS Sequence A013956 - sum of 8th powers of divisors of n, simga-8(n), 𝝈8(n).
OEIS Sequence A013957 - sum of 9th powers of divisors of n, simga-9(n), 𝝈9(n).
OEIS Sequence A013958 - sum of 10th powers of divisors of n, simga-10(n), 𝝈10(n).
OEIS Sequence A013959 - sum of 11th powers of divisors of n, simga-11(n), 𝝈11(n).
OEIS Sequence A013960 - sum of 12th powers of divisors of n, simga-12(n), 𝝈12(n).
OEIS Sequence A013961 - sum of 13th powers of divisors of n, simga-13(n), 𝝈13(n).
OEIS Sequence A013962 - sum of 14th powers of divisors of n, simga-14(n), 𝝈14(n).
OEIS Sequence A013963 - sum of 15th powers of divisors of n, simga-15(n), 𝝈15(n).
OEIS Sequence A013964 - sum of 16th powers of divisors of n, simga-16(n), 𝝈16(n).
OEIS Sequence A013965 - sum of 17th powers of divisors of n, simga-17(n), 𝝈17(n).
OEIS Sequence A013966 - sum of 18th powers of divisors of n, simga-18(n), 𝝈18(n).
OEIS Sequence A013967 - sum of 19th powers of divisors of n, simga-19(n), 𝝈19(n).
OEIS Sequence A013968 - sum of 20th powers of divisors of n, simga-20(n), 𝝈20(n).
Link to this section Functions
OEIS Sequence A001158 - Sum of cubes of divisors of N, simga-3(n), 𝝈3(n).
From OEIS A001158:
sigma_3(n): sum of cubes of divisors of n. (Formerly M4605 N1964)
Sequence IDs: :a001158
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a001158) |> Sequence.take!(10)
[1, 9, 28, 73, 126, 252, 344, 585, 757, 1134]OEIS Sequence A001159 - sum of 4th powers of divisors of n, simga-4(n), 𝝈4(n).
From OEIS A001159:
sigma_4(n): sum of 4th powers of divisors of n. (Formerly M5041 N2177)
Sequence IDs: :a001159
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a001159) |> Sequence.take!(10)
[1, 17, 82, 273, 626, 1394, 2402, 4369, 6643, 10642]OEIS Sequence A001160 - sum of 5th powers of divisors of n, simga-5(n), 𝝈5(n).
From OEIS A001160:
sigma_5(n): sum of 5th powers of divisors of n. (Formerly M5240 N2279)
Sequence IDs: :a001160
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a001160) |> Sequence.take!(10)
[1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158]OEIS Sequence A002093 - Highly Abundant Numbers
From OEIS A002093:
Highly abundant numbers: numbers n such that sigma(n) > sigma(m) for all m < n. (Formerly M0553 N0200)
Sequence IDs: :a002093
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a002093) |> Sequence.take!(25)
[1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168]OEIS Sequence A003601 - Arithmetic Numbers
From OEIS A003601:
Numbers n such that the average of the divisors of n is an integer: sigma_0(n) divides sigma_1(n). Alternatively, tau(n) (A000005(n)) divides sigma(n) (A000203(n)). (Formerly M2389)
Sequence IDs: :a003601
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a003601) |> Sequence.take!(10)
[1, 3, 5, 6, 7, 11, 13, 14, 15, 17]OEIS Sequence A013954 - sum of 6th powers of divisors of n, simga-6(n), 𝝈6(n).
From OEIS A013954:
sigma_6(n): sum of 6th powers of divisors of n.
Sequence IDs: :a013954
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013954) |> Sequence.take!(10)
[1, 65, 730, 4161, 15626, 47450, 117650, 266305, 532171, 1015690]OEIS Sequence A013955 - sum of 7th powers of divisors of n, simga-7(n), 𝝈7(n).
From OEIS A013955:
sigma_7(n): sum of 7th powers of divisors of n.
Sequence IDs: :a013955
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013955) |> Sequence.take!(10)
[1, 129, 2188, 16513, 78126, 282252, 823544, 2113665, 4785157, 10078254]OEIS Sequence A013956 - sum of 8th powers of divisors of n, simga-8(n), 𝝈8(n).
From OEIS A013956:
sigma_8(n): sum of 8th powers of divisors of n.
Sequence IDs: :a013956
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013956) |> Sequence.take!(10)
[1, 257, 6562, 65793, 390626, 1686434, 5764802, 16843009, 43053283, 100390882]OEIS Sequence A013957 - sum of 9th powers of divisors of n, simga-9(n), 𝝈9(n).
From OEIS A013957:
sigma_9(n): sum of 9th powers of divisors of n.
Sequence IDs: :a013957
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013957) |> Sequence.take!(10)
[1, 513, 19684, 262657, 1953126, 10097892, 40353608, 134480385, 387440173, 1001953638]OEIS Sequence A013958 - sum of 10th powers of divisors of n, simga-10(n), 𝝈10(n).
From OEIS A013958:
sigma_10(n): sum of 10th powers of divisors of n.
Sequence IDs: :a013958
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013958) |> Sequence.take!(10)
[1, 1025, 59050, 1049601, 9765626, 60526250, 282475250, 1074791425, 3486843451, 10009766650]OEIS Sequence A013959 - sum of 11th powers of divisors of n, simga-11(n), 𝝈11(n).
From OEIS A013959:
sigma_11(n): sum of 11th powers of divisors of n.
Sequence IDs: :a013959
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013959) |> Sequence.take!(10)
[1, 2049, 177148, 4196353, 48828126, 362976252, 1977326744, 8594130945, 31381236757, 100048830174]OEIS Sequence A013960 - sum of 12th powers of divisors of n, simga-12(n), 𝝈12(n).
From OEIS A013960:
sigma_12(n): sum of 12th powers of divisors of n.
Sequence IDs: :a013960
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013960) |> Sequence.take!(10)
[1, 4097, 531442, 16781313, 244140626, 2177317874, 13841287202, 68736258049, 282430067923, 1000244144722]OEIS Sequence A013961 - sum of 13th powers of divisors of n, simga-13(n), 𝝈13(n).
From OEIS A013961:
sigma_13(n): sum of 13th powers of divisors of n.
Sequence IDs: :a013961
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013961) |> Sequence.take!(10)
[1, 8193, 1594324, 67117057, 1220703126, 13062296532, 96889010408, 549822930945, 2541867422653, 10001220711318]OEIS Sequence A013962 - sum of 14th powers of divisors of n, simga-14(n), 𝝈14(n).
From OEIS A013962:
sigma_14(n): sum of 14th powers of divisors of n.
Sequence IDs: :a013962
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013962) |> Sequence.take!(10)
[1, 16385, 4782970, 268451841, 6103515626, 78368963450, 678223072850, 4398314962945, 22876797237931, 100006103532010]OEIS Sequence A013963 - sum of 15th powers of divisors of n, simga-15(n), 𝝈15(n).
From OEIS A013963:
sigma_15(n): sum of 15th powers of divisors of n.
Sequence IDs: :a013963
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013963) |> Sequence.take!(10)
[1, 32769, 14348908, 1073774593, 30517578126, 470199366252, 4747561509944, 35185445863425, 205891146443557, 1000030517610894]OEIS Sequence A013964 - sum of 16th powers of divisors of n, simga-16(n), 𝝈16(n).
From OEIS A013964:
sigma_16(n): sum of 16th powers of divisors of n.
Sequence IDs: :a013964
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013964) |> Sequence.take!(10)
[1, 65537, 43046722, 4295032833, 152587890626, 2821153019714, 33232930569602, 281479271743489, 1853020231898563, 10000152587956162]OEIS Sequence A013965 - sum of 17th powers of divisors of n, simga-17(n), 𝝈17(n).
From OEIS A013965:
sigma_17(n): sum of 17th powers of divisors of n.
Sequence IDs: :a013965
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013965) |> Sequence.take!(10)
[1, 131073, 129140164, 17180000257, 762939453126, 16926788715972, 232630513987208, 2251816993685505, 16677181828806733, 100000762939584198]OEIS Sequence A013966 - sum of 18th powers of divisors of n, simga-18(n), 𝝈18(n).
From OEIS A013966:
sigma_18(n): sum of 18th powers of divisors of n.
Sequence IDs: :a013966
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013966) |> Sequence.take!(10)
[1, 262145, 387420490, 68719738881, 3814697265626, 101560344351050, 1628413597910450, 18014467229220865, 150094635684419611, 1000003814697527770]OEIS Sequence A013967 - sum of 19th powers of divisors of n, simga-19(n), 𝝈19(n).
From OEIS A013967:
sigma_19(n): sum of 19th powers of divisors of n.
Sequence IDs: :a013967
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013967) |> Sequence.take!(10)
[1, 524289, 1162261468, 274878431233, 19073486328126, 609360902796252, 11398895185373144, 144115462954287105, 1350851718835253557, 10000019073486852414]OEIS Sequence A013968 - sum of 20th powers of divisors of n, simga-20(n), 𝝈20(n).
From OEIS A013968:
sigma_20(n): sum of 20th powers of divisors of n.
Sequence IDs: :a013968
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Sigma, :a013968) |> Sequence.take!(10)
[1, 1048577, 3486784402, 1099512676353, 95367431640626, 3656161927895954, 79792266297612002, 1152922604119523329, 12157665462543713203, 100000095367432689202]