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

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

Author

Colin Barker, Sep 13 2016

Keywords

• nonn

Examples

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

Links

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

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)).