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

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

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Formula

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

Example

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

Mathematica

DivisorSigma[0, PolygonalNumber[5, Range[80]]] (* Harvey P. Dale, Jul 19 2025 *)

Prog

(PARI)
pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
vector(100, n, numdiv(pg(5, n)))

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).

Sequence in context: A029670 A160205 A187817 * A276680 A053794 A249913

Adjacent sequences: A276675 A276676 A276677 * A276679 A276680 A276681

Keyword

nonn

Author

Colin Barker, Sep 13 2016

Status

approved