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

Author

Colin Barker, Sep 13 2016

Keywords

• nonn

Examples

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

Links

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

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