A366656 Number of divisors of 8^n+1.

2, 3, 4, 8, 4, 12, 16, 12, 8, 20, 48, 24, 16, 12, 64, 64, 8, 48, 64, 24, 16, 64, 64, 24, 32, 96, 768, 192, 32, 24, 1536, 24, 8, 256, 512, 1536, 64, 96, 256, 64, 64, 96, 1024, 48, 128, 1280, 256, 96, 128, 96, 8192, 1024, 32, 48, 1024, 2304, 256, 192, 256, 192

Offset: 0

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Examples

			a(4)=4 because 8^4+1 has divisors {1, 17, 241, 4097}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..502

Crossrefs

Cf. A062395, A000005, A057936, A274905, A366653, A366638, A366655, A366657, A366658.

Cf. A046798, A366577, A366606, A366616, A366628, A366637, A366665, A344897, A366688, A366714.

Programs

Maple

a:=n->numtheory[tau](8^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[0, 8^Range[0,59] + 1] (* Paul F. Marrero Romero, Nov 12 2023 *)

PARI

a(n) = numdiv(8^n+1);

Formula

a(n) = sigma0(8^n+1) = A000005(A062395(n)).

a(n) = A046798(3*n). - Max Alekseyev, Jan 09 2024