A366653 Sum of the divisors of 8^n-1.

8, 104, 592, 8736, 38912, 473600, 2466048, 38054016, 155493536, 2015330304, 10359014400, 166290432000, 636328345600, 7645340651520, 42424026529792, 648494317126656, 2599936977797120, 32817383473149440, 164708609085669376, 3010983668199456768

Offset: 1

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Examples

			a(5)=38912 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, A000203, A057953, A059890, A366651, A366652, A366654.

Cf. A075708, A366576, A366603, A366613, A366622, A366634, A366662, A102146, A366684, A366710.

Programs

Maple

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

Mathematica

DivisorSigma[1, 8^Range[30]-1]

SageMath

[sigma(8**n-1, 1) for n in range(1, 21)] # Stefano Spezia, Aug 02 2025

Formula

a(n) = sigma(8^n-1) = A000203(A024088(n)).

a(n) = A075708(3*n). - Max Alekseyev, Jan 09 2024