A366714 Number of divisors of 12^n+1.

2, 2, 4, 8, 4, 4, 8, 8, 8, 32, 12, 4, 16, 24, 16, 128, 4, 8, 32, 16, 64, 384, 64, 16, 64, 64, 32, 1024, 8, 8, 48, 8, 4, 512, 16, 32, 128, 16, 32, 1536, 16, 32, 64, 32, 16, 4096, 8, 32, 32, 32, 512, 512, 32, 32, 1024, 128, 512, 1536, 192, 64, 1024, 32, 64

Offset: 0

Author

Sean A. Irvine, Oct 17 2023

Keywords

• nonn

Examples

			a(4)=4 because 12^4+1 has divisors {1, 89, 233, 20737}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..306

Crossrefs

Cf. A178248, A000005, A046798, A344897, A366709, A366712, A366713, A366715, A366716, A366719, A366720, A366688.

Programs

Maple

a:=n->numtheory[tau](12^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[0, 12^Range[0, 70] + 1] (* Paolo Xausa, Apr 20 2025 *)

PARI

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

Formula

a(n) = sigma0(12^n+1) = A000005(A178248(n)).