A366616 Number of divisors of 5^n+1.

2, 4, 4, 12, 4, 8, 8, 16, 8, 32, 16, 32, 8, 16, 8, 96, 8, 16, 32, 32, 16, 576, 16, 16, 16, 32, 24, 320, 8, 16, 128, 32, 16, 384, 64, 128, 64, 32, 16, 192, 32, 64, 64, 64, 8, 512, 8, 32, 32, 128, 128, 768, 32, 32, 64, 128, 128, 384, 8, 64, 64, 64, 16, 24576, 16

Offset: 0

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(3)=12 because 5^3+1 has divisors {1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..471

Crossrefs

Cf. A000005, A034474, A057939, A074478, A366612, A366607, A366615, A366617, A366618.

Cf. A046798, A366577, A366606, A366628, A366637, A366656, A366665, A344897, A366688, A366714.

Programs

Maple

a:=n->numtheory[tau](5^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[0, 5^Range[0, 70] + 1] (* Paolo Xausa, Apr 20 2025 *)

PARI

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

Formula

a(n) = sigma0(5^n+1) = A000005(A034474(n)).