A366661 Number of divisors of 9^n-1.

4, 10, 16, 24, 24, 80, 16, 112, 128, 180, 64, 384, 16, 160, 768, 256, 128, 1280, 64, 864, 768, 640, 32, 14336, 384, 160, 4096, 1536, 256, 23040, 128, 576, 2048, 1280, 768, 12288, 128, 640, 12288, 16128, 128, 61440, 32, 12288, 196608, 320, 512, 131072, 2048

Offset: 1

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Examples

			a(2)=10 because 9^2-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..690

Crossrefs

Cf. A024101, A000005, A057952, A366660, A366662, A366663.

Cf. A046801, A366575, A366602, A366612, A366621, A366633, A366652, A070528, A366683, A366709.

Programs

Maple

a:=n->numtheory[tau](9^n-1):
seq(a(n), n=1..100);

Mathematica

DivisorSigma[0, 9^Range[100]-1]

PARI

a(n) = numdiv(9^n-1);

Formula

a(n) = sigma0(9^n-1) = A000005(A024101(n)).

a(n) = A366575(2*n) = A366575(n) * A366577(n) * (4 + A007814(n)) / (2 * (3 + A007814(n))). - Max Alekseyev, Jan 07 2024