chunky v0.9.0 Chunky.Sequence.OEIS.Core View Source
OEIS Core Sequences.
Available Sequences
- A000005 - Divisors of N -
:a000005
-create_sequence_a000005/1
- A000009 - Number of partitions of n into distinct parts -
:a000009
-create_sequence_a000009/1
- A000010 - Euler's totient function -
:a000010
-create_sequence_a000010/1
- A000041 - Partition Numbers -
:a000041
-create_sequence_a000041/1
- A000079 - Powers of 2 -
:a000079
-create_sequence_a000079/1
- A000203 - Sum of Divisors -
:a000203
-create_sequence_a000203/1
- A000396 - Perfect Numbers -
:a000396
-create_sequence_a000396/1
- A000593 - Sum of Odd Divisors of N -
:a000593
-create_sequence_a000593/1
- A001065 - Sum of proper divisors (Aliquot parts) of N. -
:a001065
-create_sequence_a001065/1
- A001157 - Sum of squares of divisors of N -
:a001157
-create_sequence_a001157/1
- A005100 - Deficient Numbers -
:a005100
-create_sequence_a005100/1
- A005101 - Abundant Numbers -
:a005101
-create_sequence_a005101/1
Link to this section Summary
Functions
OEIS Sequence A000005
- Number of divisors of N, simga-0(n), 𝝈0(n)
.
OEIS Sequence A000009
- Number of partitions of n into distinct parts
OEIS Sequence A000010
- Euler's totient function phi(n)
OEIS Sequence A000041
- Partitions of integer N
OEIS Sequence A000079
- Powers of 2 a(n) = 2^n
OEIS Sequence A000203
- Sum of Divisors σ1(n)
OEIS Sequence A000396
- Perfect Numbers
OEIS Sequence A000593
- Sum of Odd Divisors of N
OEIS Sequence A001065
- Sum of proper divisors (Aliquot parts) of N.
OEIS Sequence A001157
- Sum of squares of divisors of N, simga-2(n), 𝝈2(n)
.
OEIS Sequence A005100
- Deficient Numbers
OEIS Sequence A005101
- Abundant Numbers
Link to this section Functions
OEIS Sequence A000005
- Number of divisors of N, simga-0(n), 𝝈0(n)
.
From OEIS A000005:
d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n. (Formerly M0246 N0086)
Sequence IDs: :a000005
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000005) |> Sequence.take!(10)
[1, 2, 2, 3, 2, 4, 2, 4, 3, 4]
OEIS Sequence A000009
- Number of partitions of n into distinct parts
From OEIS A000009:
Expansion of Product_{m >= 1} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts (if n > 0). (Formerly M0281 N0100)
Divergence
Calculation of this sequence is based on translation of a Maxima program by Vladimir Kruchinin,
and diverges from canonical results for n > 10
.
Sequence IDs: :a000009
Finite: False
Offset: 0
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000009) |> Sequence.take!(10)
[1, 1, 1, 2, 2, 3, 4, 5, 6, 8]
OEIS Sequence A000010
- Euler's totient function phi(n)
From OEIS A000010:
Euler totient function phi(n): count numbers <= n and prime to n. (Formerly M0299 N0111)
Sequence IDs: :a000010
Finite: false
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000010) |> Sequence.take!(20)
[1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 6, 8, 8, 16, 6, 18, 8]
OEIS Sequence A000041
- Partitions of integer N
This sequence contains the partitions of the integers from 0
to 250
.
From Wikipedia:
In number theory, the partition function
p(n)
represents the number of possible partitions of a non-negative integern
. For instance,p(4) = 5
because the integer4
has the five partitions:1 + 1 + 1 + 1
,1 + 1 + 2
,1 + 3
,2 + 2
, and4
.
From OEIS A000041:
a(n) is the number of partitions of n (the partition numbers). (Formerly M0663 N0244)
Sequence IDs: :a000041
Finite: true
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000041) |> Sequence.take!(10)
[1, 1, 2, 3, 5, 7, 11, 15, 22, 30]
OEIS Sequence A000079
- Powers of 2 a(n) = 2^n
From OEIS A000009:
Powers of 2: a(n) = 2^n. (Formerly M1129 N0432)
Sequence IDs: :a000079
Finite: False
Offset: 0
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000079) |> Sequence.take!(20)
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288]
OEIS Sequence A000203
- Sum of Divisors σ1(n)
From OEIS A000203:
(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n). (Formerly M2329 N0921)
Sequence IDs: :a000203
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000203) |> Sequence.take!(20)
[1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42]
OEIS Sequence A000396
- Perfect Numbers
From OEIS A000396:
Perfect numbers n: n is equal to the sum of the proper divisors of n. (Formerly M4186 N1744)
Sequence IDs: :a000396
Finite: True
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000396) |> Sequence.take!(5)
[6, 28, 496, 8128, 33550336]
OEIS Sequence A000593
- Sum of Odd Divisors of N
From OEIS A000593:
Sum of odd divisors of n. (Formerly M3197 N1292)
Sequence IDs: :a000593
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a000593) |> Sequence.take!(10)
[1, 1, 4, 1, 6, 4, 8, 1, 13, 6]
OEIS Sequence A001065
- Sum of proper divisors (Aliquot parts) of N.
From OEIS A001065:
Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n. (Formerly M2226 N0884)
Sequence IDs: :a001065
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a001065) |> Sequence.take!(20)
[0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22]
OEIS Sequence A001157
- Sum of squares of divisors of N, simga-2(n), 𝝈2(n)
.
From OEIS A001157:
sigma_2(n): sum of squares of divisors of n. (Formerly M3799 N1551)
Sequence IDs: :a001157
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a001157) |> Sequence.take!(10)
[1, 5, 10, 21, 26, 50, 50, 85, 91, 130]
OEIS Sequence A005100
- Deficient Numbers
From OEIS A005100:
Deficient numbers: numbers n such that sigma(n) < 2n. (Formerly M0514)
Sequence IDs: :a005100
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a005100) |> Sequence.take!(25)
[1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32]
OEIS Sequence A005101
- Abundant Numbers
From OEIS A005101:
Abundant numbers (sum of divisors of n exceeds 2n). (Formerly M4825)
Sequence IDs: :a005101
Finite: False
Offset: 1
Example
iex> Sequence.create(Sequence.OEIS.Core, :a005101) |> Sequence.take!(10)
[12, 18, 20, 24, 30, 36, 40, 42, 48, 54]