A366662 Sum of the divisors of 9^n-1.

15, 186, 1680, 15876, 123690, 1541568, 8992680, 111757968, 967814400, 9366647892, 62424587520, 852903426816, 4766016364260, 55176998178240, 550081165885440, 4829754617483040, 31725040326819840, 471309320999516160, 2535353780263288800, 33995669076586206864

Offset: 1

Author

Sean A. Irvine, Oct 15 2023

Keywords

• nonn

Examples

			a(2)=186 because 9^2-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..690

Crossrefs

Cf. A024101, A000203, A366660, A366661, A366663.

Cf. A075708, A366576, A366603, A366613, A366622, A366634, A366653, A102146, A366684, A366710.

Programs

Maple

a:=n->numtheory[sigma](9^n-1):
seq(a(n), n=1..30);

Mathematica

DivisorSigma[1, 9^Range[30]-1]

Formula

a(n) = sigma(9^n-1) = A000203(A024101(n)).

a(n) = A366576(2*n) = A366576(n) * A366578(n) * (2^(4 + A007814(n)) - 1) / (2^(3 + A007814(n)) - 1) / 3. - Max Alekseyev, Jan 07 2024