A366633 Number of divisors of 7^n-1.

4, 10, 12, 36, 8, 60, 16, 84, 64, 80, 16, 864, 8, 160, 96, 384, 16, 640, 16, 1536, 96, 160, 32, 16128, 32, 80, 1280, 1152, 32, 3840, 32, 1728, 384, 80, 128, 18432, 32, 160, 192, 14336, 32, 7680, 16, 4608, 2048, 160, 16, 147456, 256, 640, 768, 1152, 32, 25600

Offset: 1

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(5)=8 because 7^5-1 has divisors {1, 2, 3, 6, 2801, 5602, 8403, 168061}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..388

Crossrefs

Cf. A024075, A000005, A057954, A059889, A074249, A218358, A366632, A366634, A366635.

Cf. A046801, A366575, A366602, A366612, A366621, A366652, A366661, A070528, A366683, A366709.

Programs

Maple

a:=n->numtheory[tau](7^n-1):
seq(a(n), n=1..100);

Mathematica

DivisorSigma[0, 7^Range[100]-1]

PARI

a(n) = numdiv(7^n-1);

Formula

a(n) = sigma0(7^n-1) = A000005(A024075(n)).