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

Author

Vaclav Kotesovec, Aug 18 2021

Keywords

• nonn

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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