A366621 Number of divisors of 6^n-1.

2, 4, 4, 8, 6, 16, 4, 16, 16, 48, 8, 128, 8, 48, 48, 64, 32, 128, 8, 384, 16, 32, 32, 512, 32, 128, 64, 384, 4, 1536, 8, 512, 64, 256, 96, 8192, 64, 64, 64, 3072, 8, 768, 32, 512, 1536, 256, 16, 8192, 32, 512, 512, 2048, 16, 2048, 96, 12288, 128, 64, 16

Offset: 1

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(4)=8 because 6^4-1 has divisors {1, 5, 7, 35, 37, 185, 259, 1295}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..430

Crossrefs

Cf. A024062, A000005, A057955, A059888, A274907, A366613, A366620, A366622, A366623.

Cf. A046801, A366575, A366602, A366612, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

Maple

a:=n->numtheory[tau](6^n-1):
seq(a(n), n=1..100);

Mathematica

DivisorSigma[0, 6^Range[100]-1]

PARI

a(n) = numdiv(6^n-1);

Formula

a(n) = sigma0(6^n-1) = A000005(A024062(n)).