chunky v0.9.0 Chunky.Sequence.OEIS.Factors View Source
OEIS Sequences dealing with Factors, Factorization, and properties of integer factors.
Available Sequences
- A001597 - Perfect Powers -
:a001597
-create_sequence_a001597/1
- A001694 - Powerful Numbers -
:a001694
-create_sequence_a001694/1
- A002182 - Highly composite numbers: numbers with record value -
:a002182
-create_sequence_a002182/1
- A002473 - 7-smooth Numbers -
:a002473
-create_sequence_a03586/1
- A003586 - 3-smooth Numbers -
:a003586
-create_sequence_a03586/1
- A005361 - Product of Expoenents of prime factors of N -
:a005361
-create_sequence_a005361/1
- A005934 - Highly powerful numbers: numbers with record value -
:a005934
-create_sequence_a005934/1
- A051037 - 5-smooth Numbers -
:a051037
-create_sequence_a03586/1
- A051038 - 11-smooth Numbers -
:a051038
-create_sequence_a03586/1
- A052486 - Achilles numbers - powerful but imperfect -
:a052486
-create_sequence_a052486/1
- A080197 - 13-smooth Numbers -
:a080197
-create_sequence_a03586/1
- A080681 - 17-smooth Numbers -
:a080681
-create_sequence_a03586/1
- A080682 - 29-smooth Numbers -
:a080682
-create_sequence_a03586/1
- A080683 - 23-smooth Numbers -
:a080683
-create_sequence_a03586/1
Link to this section Summary
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
Link to this section Functions
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]
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]