chunky v0.9.0 Chunky.Sequence.OEIS.Factors View Source

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

Available Sequences

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Functions

OEIS Sequence A001597 - Perfect Powers

OEIS Sequence A001694 - Powerful Numbers

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

OEIS Sequence A002473 - 7-smooth Numbers

OEIS Sequence A003586 - 3-smooth Numbers

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

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

OEIS Sequence A051037 - 5-smooth Numbers

OEIS Sequence A051038 - 11-smooth Numbers

OEIS Sequence A052486 - Achilles numbers - powerful but imperfect

OEIS Sequence A080197 - 13-smooth Numbers

OEIS Sequence A080681 - 17-smooth Numbers

OEIS Sequence A080682 - 19-smooth Numbers

OEIS Sequence A080683 - 23-smooth Numbers

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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_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_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_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_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_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]
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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]
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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]