A366603 Sum of the divisors of 4^n-1.

4, 24, 104, 432, 1536, 8736, 22528, 111456, 473600, 1999872, 5909760, 38054016, 89522176, 462274560, 2015330304, 7304603328, 22907191296, 166290432000, 366506672128, 2220409884672, 7645340651520, 29833839544320, 95821839806976, 648494317126656

Offset: 1

Author

Sean A. Irvine, Oct 14 2023

Keywords

• nonn

Examples

			a(4)=432 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 (terms 1..1062 from Robert Israel)

Crossrefs

Cf. A024036, A000203, A057957, A069061, A075708, A295501, A366602, A366604.

Cf. A075708, A366576, A366613, A366622, A366634, A366653, A366662, A102146, A366684, A366710.

Programs

Maple

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

Mathematica

DivisorSigma[1,4^Range[30]-1] (* Paolo Xausa, Oct 14 2023 *)

Formula

a(n) = sigma(4^n-1) = A000203(A024036(n)).

a(n) = A069061(n) * A075708(n). - Robert Israel, Nov 22 2023