A374973 a(n) = Sum_{k=1..n-1} tau(k) * sigma_2(n-k).

0, 1, 7, 22, 54, 105, 188, 307, 459, 690, 937, 1307, 1680, 2260, 2740, 3588, 4221, 5402, 6163, 7714, 8694, 10723, 11758, 14449, 15574, 18884, 20320, 24228, 25626, 30768, 32038, 37985, 39826, 46515, 47898, 56877, 57754, 67433, 69450, 80062, 81103, 95034, 94941

Offset: 1

Author

Seiichi Manyama, Jul 26 2024

Keywords

• nonn
• easy

Comments

Convolution of tau with sigma_2.

Crossrefs

Cf. A000005, A001157, A055507, A191831.

Programs

PARI

a(n) = sum(k=1, n-1, sigma(k, 0)*sigma(n-k, 2));

PARI

my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^k/(1-x^k))*sum(k=1, N, k^2*x^k/(1-x^k))))

Formula

G.f.: ( Sum_{k>=1} x^k/(1 - x^k) ) * ( Sum_{k>=1} k^2 * x^k/(1 - x^k) ).