A366577 Number of divisors of 3^n+1.

2, 3, 4, 6, 4, 6, 8, 6, 8, 24, 12, 12, 8, 6, 16, 48, 4, 24, 16, 12, 8, 72, 16, 6, 64, 24, 16, 96, 16, 24, 48, 12, 4, 96, 16, 24, 16, 24, 16, 192, 32, 12, 128, 6, 32, 768, 16, 24, 16, 24, 128, 384, 16, 12, 32, 96, 64, 192, 16, 12, 128, 12, 32, 4608, 4, 24, 64

Offset: 0

Author

Sean A. Irvine, Oct 13 2023

Keywords

• nonn

Examples

			a(4)=4 because 3^4+1 has divisors {1, 2, 41, 82}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 0..691

Crossrefs

Cf. A000005, A002592, A034472, A046798, A057935, A057941, A074476, A274909, A366575, A366578, A366579, A366580

Programs

Maple

a:=n->numtheory[tau](3^n+1):
seq(a(n), n=0..100);

Mathematica

DivisorSigma[0,3^Range[0,100]+1] (* Paolo Xausa, Oct 15 2023 *)

PARI

a(n) = numdiv(3^n+1); \\ Michel Marcus, Oct 14 2023

Formula

a(n) = sigma0(3^n+1) = A000005(A034472(n)).