A366602 Number of divisors of 4^n-1.

2, 4, 6, 8, 8, 24, 8, 16, 32, 48, 16, 96, 8, 64, 96, 32, 8, 512, 8, 192, 144, 128, 16, 768, 128, 128, 160, 256, 64, 4608, 8, 128, 384, 128, 512, 8192, 32, 128, 192, 768, 32, 9216, 32, 1024, 4096, 512, 64, 6144, 32, 8192, 1536, 1024, 64, 10240, 3072, 2048, 384

Offset: 1

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(4)=8 because 4^4-1 has divisors {1, 3, 5, 15, 17, 51, 85, 255}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..1128

Crossrefs

Cf. A024036, A000005, A057957, A295501, A366603, A366604.

Cf. A046798, A046801, A366575, A366612, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

Maple

a:=n->numtheory[tau](4^n-1):
seq(a(n), n=1..100);

Mathematica

DivisorSigma[0,4^Range[100]-1] (* Paolo Xausa, Oct 14 2023 *)

PARI

a(n) = numdiv(4^n-1);

Formula

a(n) = sigma0(4^n-1) = A000005(A024036(n)).

a(n) = A046801(2*n) = A046798(n) * A046801(n). - Max Alekseyev, Jan 07 2024