A366628 Number of divisors of 6^n+1.

2, 2, 2, 4, 2, 8, 8, 12, 4, 8, 8, 4, 4, 16, 8, 32, 8, 8, 64, 8, 8, 48, 16, 8, 16, 16, 16, 32, 32, 16, 512, 4, 8, 64, 8, 1536, 32, 16, 8, 512, 32, 16, 128, 4, 8, 128, 32, 4, 128, 64, 64, 256, 16, 32, 1024, 192, 64, 128, 8, 4, 64, 8, 4, 768, 8, 256, 2048, 32, 32

Offset: 0

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(3)=4 because 6^3+1 has divisors {1, 7, 31, 217}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..430

Crossrefs

Cf. A062394, A000005, A057938, A366621, A366627, A366629, A366630, A366670.

Cf. A046798, A366577, A366606, A366616, A366637, A366656, A366665, A344897, A366688, A366714.

Programs

Maple

a:=n->numtheory[tau](6^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[0, 6^Range[0, 70] + 1] (* Paolo Xausa, Apr 19 2025 *)

PARI

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

Formula

a(n) = sigma0(6^n+1) = A000005(A062394(n)).