A347108 a(n) = Sum_{k=1..n} sigma(k)*sigma(2*k), where sigma(n) = A000203(n) is the sum of the divisors of n.

3, 24, 72, 177, 285, 621, 813, 1278, 1785, 2541, 2973, 4653, 5241, 6585, 8313, 10266, 11238, 14787, 15987, 19767, 22839, 25863, 27591, 35031, 37914, 42030, 46830, 53550, 56250, 68346, 71418, 79419, 86331, 93135, 100047, 117792, 122124, 130524, 139932, 156672

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Formula

a(n) ~ 2*zeta(3)*n^3.

Mathematica

Accumulate[Table[DivisorSigma[1, k] * DivisorSigma[1, 2*k], {k, 1, 100}]]

Prog

(PARI) a(n) = sum(k=1, n, sigma(k)*sigma(2*k)); \\ Michel Marcus, Aug 18 2021

Crossrefs

Cf. A000203, A024916, A065764, A072379, A074285, A326123, A326124, A330322, A346865.

Sequence in context: A369953 A162654 A092468 * A027158 A251781 A117642

Adjacent sequences: A347105 A347106 A347107 * A347109 A347110 A347111

Keyword

nonn

Author

Vaclav Kotesovec, Aug 18 2021

Status

approved