A366575 Number of divisors of 3^n - 1.

2, 4, 4, 10, 6, 16, 4, 24, 8, 24, 8, 80, 4, 16, 24, 112, 8, 128, 8, 180, 16, 64, 8, 384, 24, 16, 64, 160, 16, 768, 16, 256, 32, 128, 48, 1280, 8, 64, 96, 864, 16, 768, 8, 640, 384, 32, 32, 14336, 128, 384, 64, 160, 16, 4096, 128, 1536, 128, 256, 8, 23040, 8

Offset: 1

Author

Sean A. Irvine, Oct 13 2023

Keywords

• nonn

Examples

			a(4)=10 because 3^4-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..690

Crossrefs

Cf. A024023, A000005, A046801, A133801, A295500, A366576.

Cf. A046801, A366602, A366612, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

Maple

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

Mathematica

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

Formula

a(n) = sigma0(3^n-1) = A000005(A024023).