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

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

Author

Colin Barker, Sep 13 2016

Keywords

• nonn

Examples

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

Links

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

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)).