A366709 Number of divisors of 12^n-1.

2, 4, 4, 16, 4, 32, 8, 64, 16, 16, 12, 256, 8, 64, 64, 512, 8, 512, 4, 192, 32, 48, 16, 4096, 16, 192, 64, 1024, 32, 8192, 32, 2048, 192, 64, 512, 16384, 8, 64, 128, 12288, 16, 12288, 32, 3072, 4096, 256, 8, 262144, 32, 1024, 64, 6144, 128, 65536, 192, 8192

Offset: 1

Author

Sean A. Irvine, Oct 17 2023

Keywords

• nonn

Examples

			a(3)=4 because 12^3-1 has divisors {1, 11, 157, 1727}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..310

Crossrefs

Cf. A000005, A024140, A046801, A070528, A366707, A366708, A366710, A366683.

Programs

Maple

a:=n->numtheory[tau](12^n-1):
seq(a(n), n=1..100);

Mathematica

DivisorSigma[0, 12^Range[100]-1]

PARI

a(n) = numdiv(12^n-1);

Formula

a(n) = sigma0(12^n-1) = A000005(A024140(n)).