A366652 Number of divisors of 8^n-1.

2, 6, 4, 24, 8, 32, 12, 96, 8, 96, 16, 512, 16, 144, 64, 768, 32, 160, 16, 4608, 96, 384, 16, 8192, 128, 192, 64, 9216, 64, 4096, 8, 6144, 256, 1536, 1536, 10240, 64, 384, 512, 73728, 32, 6144, 32, 24576, 1024, 384, 64, 262144, 64, 12288, 256, 147456, 256

Offset: 1

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Examples

			a(5)=8 because 8^5-1 has divisors {1, 7, 31, 151, 217, 1057, 4681, 32767}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A024088, A000005, A057953, A059890, A366651, A366653, A366654.

Cf. A046801, A366575, A366602, A366612, A366621, A366633, A366661, A070528, A366683, A366709.

Programs

Maple

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

Mathematica

DivisorSigma[0, 8^Range[100]-1]

PARI

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

Formula

a(n) = sigma0(8^n-1) = A000005(A024088(n)).

a(n) = A046801(3*n). - Max Alekseyev, Jan 09 2024