cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A276678 Number of divisors of the n-th pentagonal number.

Original entry on oeis.org

1, 2, 6, 4, 4, 4, 8, 6, 6, 4, 10, 16, 4, 4, 16, 8, 6, 6, 12, 8, 8, 8, 8, 12, 6, 8, 32, 8, 4, 8, 8, 20, 12, 4, 24, 12, 8, 4, 16, 24, 4, 16, 14, 8, 12, 4, 16, 32, 6, 6, 24, 16, 4, 16, 16, 12, 16, 4, 16, 16, 8, 8, 24, 12, 8, 8, 18, 16, 8, 16, 8, 36, 4, 8, 60, 8
Offset: 1

Views

Author

Colin Barker, Sep 13 2016

Keywords

Examples

			a(7) = 8 because the 7th pentagonal number is 70, which has 8 divisors: 1,2,5,7,10,14,35,70.

Links

Crossrefs

Cf. A000005, A000326 (pentagonal numbers).
Cf. A063440 (m=3), A048691 (m=4), A276679 (m=6), A276680 (m=7), A276681 (m=8), A276682 (m=9), A276683 (m=10).

Programs

  • Mathematica
    DivisorSigma[0,PolygonalNumber[5,Range[80]]] (* Harvey P. Dale, Jul 19 2025 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
vector(100, n, numdiv(pg(5,n)))

Formula

a(n) = A000005(A000326(n)). - Omar E. Pol, Sep 13 2016

A276679 Number of divisors of the n-th hexagonal number.

Original entry on oeis.org

1, 4, 4, 6, 6, 8, 4, 16, 6, 8, 8, 12, 6, 16, 8, 10, 8, 24, 4, 24, 8, 8, 12, 16, 9, 16, 8, 24, 8, 16, 4, 36, 16, 8, 16, 18, 4, 24, 16, 16, 10, 16, 8, 24, 12, 16, 8, 40, 6, 36, 8, 12, 16, 16, 8, 32, 8, 16, 12, 48, 6, 16, 24, 14, 16, 16, 8, 48, 8, 16, 8, 48, 8
Offset: 1

Views

Author

Colin Barker, Sep 13 2016

Keywords

Examples

			a(6) = 8 because the 6th hexagonal number is 66, which has 8 divisors: 1,2,3,6,11,22,33,66.

Links

Crossrefs

Cf. A000005, A000384.
Number of divisors of m-gonal numbers (m = 3..10): A063440, A048691, A276678, this sequence, A276680, A276681, A276682, A276683.

Programs

  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
vector(100, n, numdiv(pg(6,n)))

Formula

a(n) = A000005(A000384(n)). - Omar E. Pol, Sep 13 2016

A276681 Number of divisors of the n-th octagonal number.

Original entry on oeis.org

1, 4, 4, 8, 4, 12, 4, 10, 9, 16, 4, 16, 4, 20, 8, 12, 6, 24, 8, 16, 8, 16, 4, 40, 6, 16, 8, 16, 8, 40, 8, 14, 8, 24, 8, 24, 4, 24, 16, 20, 6, 32, 4, 32, 24, 20, 4, 24, 12, 24, 8, 32, 4, 56, 8, 20, 12, 16, 12, 32, 4, 20, 24, 32, 8, 48, 4, 16, 16, 48, 4, 30, 8
Offset: 1

Views

Author

Colin Barker, Sep 13 2016

Keywords

Examples

			a(4) = 8 because the 4th octagonal number is 40, which has 8 divisors: 1,2,4,5,8,10,20,40.

Links

Crossrefs

Cf. A000005, A000567.
Cf. A063440 (m=3), A048691 (m=4), A276678 (m=5), A276679 (m=6), A276680 (m=7), A276682 (m=9), A276683 (m=10).

Programs

  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
vector(150, n, numdiv(pg(8,n)))

Formula

a(n) = A000005(A000567(n)).

A276682 Number of divisors of the n-th 9-gonal number.

Original entry on oeis.org

1, 3, 8, 4, 6, 4, 8, 12, 6, 6, 18, 8, 4, 8, 16, 8, 8, 9, 14, 24, 8, 4, 16, 12, 8, 8, 24, 8, 12, 12, 8, 20, 8, 4, 48, 24, 4, 12, 16, 24, 8, 12, 12, 16, 18, 4, 20, 16, 9, 16, 40, 8, 8, 8, 24, 36, 8, 4, 24, 24, 4, 16, 24, 12, 24, 8, 16, 16, 8, 12, 16, 18, 8, 16
Offset: 1

Views

Author

Colin Barker, Sep 13 2016

Keywords

Examples

			a(2) = 3 because the 2nd 9-gonal number is 9, which has 3 divisors: 1,3,9.

Links

Crossrefs

Cf. A000005, A001106.
Cf. A063440 (m=3), A048691 (m=4), A276678 (m=5), A276679 (m=6), A276680 (m=7), A276681 (m=8), A276683 (m=10).

Programs

  • Mathematica
    DivisorSigma[0,PolygonalNumber[9,Range[80]]] (* Harvey P. Dale, Dec 02 2024 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
vector(150, n, numdiv(pg(9,n)))

Formula

a(n) = A000005(A001106(n)).

A276683 Number of divisors of the n-th 10-gonal number.

Original entry on oeis.org

1, 4, 4, 6, 4, 12, 6, 8, 8, 8, 4, 24, 6, 8, 12, 10, 8, 16, 4, 24, 12, 16, 4, 24, 6, 8, 20, 12, 4, 32, 6, 24, 12, 16, 8, 24, 8, 8, 16, 16, 8, 48, 6, 12, 16, 8, 8, 50, 6, 12, 12, 24, 8, 20, 16, 32, 24, 8, 4, 36, 4, 24, 16, 28, 8, 32, 8, 12, 24, 16, 4, 64, 6, 8
Offset: 1

Views

Author

Colin Barker, Sep 13 2016

Keywords

Examples

			a(4) = 6 because the 4th 10-gonal number is 52, which has 6 divisors: 1,2,4,13,26,52.

Links

Crossrefs

Cf. A000005, A001107.
Cf. A063440 (m=3), A048691 (m=4), A276678 (m=5), A276679 (m=6), A276680 (m=7), A276681 (m=8), A276682 (m=9).

Programs

  • Mathematica
    DivisorSigma[0,PolygonalNumber[10,Range[80]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 05 2021 *)
  • PARI
    pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
vector(150, n, numdiv(pg(10,n)))

Formula

a(n) = A000005(A001107(n)).
Showing 1-5 of 5 results.

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