A366665 Number of divisors of 9^n+1.

2, 4, 4, 8, 8, 12, 8, 16, 4, 16, 8, 16, 64, 16, 16, 48, 4, 16, 16, 16, 32, 128, 32, 16, 16, 128, 16, 32, 64, 16, 128, 32, 4, 64, 32, 384, 256, 32, 64, 128, 32, 32, 1024, 128, 64, 384, 16, 16, 64, 512, 64, 256, 128, 64, 512, 192, 512, 512, 32, 8, 2048, 64, 16

Offset: 0

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Examples

			a(2)=4 because 9^2+1 has divisors {1, 2, 41, 82}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..345

Crossrefs

Cf. A062396, A000005, A057935, A366661, A366664, A366666, A366667.

Cf. A046798, A366577, A366606, A366616, A366628, A366637, A366656, A344897, A366688, A366714.

Programs

Maple

a:=n->numtheory[tau](9^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[0, 9^Range[0,62] + 1] (* Paul F. Marrero Romero, Nov 13 2023 *)

PARI

a(n) = numdiv(9^n+1);

Formula

a(n) = sigma0(9^n+1) = A000005(A062396(n)).

a(n) = A366577(2*n). - Max Alekseyev, Jan 08 2024