A366612 Number of divisors of 5^n-1.

3, 8, 6, 20, 12, 48, 6, 48, 24, 64, 6, 240, 6, 64, 96, 224, 12, 512, 24, 640, 48, 128, 12, 1152, 192, 64, 384, 320, 24, 6144, 12, 1024, 48, 128, 384, 10240, 24, 512, 48, 6144, 12, 18432, 12, 1280, 3072, 128, 6, 10752, 12, 4096, 192, 960, 24, 81920, 576, 1536

Offset: 1

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(3)=6 because 5^3-1 has divisors {1, 2, 4, 31, 62, 124}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..502

Crossrefs

Cf. A024049, A000005, A057956, A059887, A074479, A143665, A295502, A218357, A366611, A366613.

Cf. A046801, A366575, A366602, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

Maple

a:=n->numtheory[tau](5^n-1):
seq(a(n), n=1..100);

Mathematica

DivisorSigma[0, 5^Range[100]-1]

PARI

a(n) = numdiv(5^n-1);

Formula

a(n) = sigma0(5^n-1) = A000005(A024049(n)).