A356038 a(n) = Sum_{k=1..n} binomial(n,k) * sigma_2(k).

1, 7, 28, 95, 286, 802, 2143, 5519, 13807, 33762, 81060, 191678, 447396, 1032647, 2360593, 5351231, 12041764, 26920297, 59829006, 132262550, 290990077, 637429514, 1390811841, 3023647046, 6551547161, 14151910442, 30481920523, 65480947739, 140318385088, 299995596747

Offset: 1

Author

Vaclav Kotesovec, Jul 24 2022

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Divisor Function.

Crossrefs

Cf. A001157, A160399, A185003, A356039.

Cf. A006218, A024916, A064602, A064603.

Programs

Maple

with(numtheory): seq(add(sigma[2](i)*binomial(n,i),i=1..n), n=1..60); # Ridouane Oudra, Oct 25 2022

Mathematica

Table[Sum[Binomial[n, k] * DivisorSigma[2, k], {k, 1, n}], {n, 1, 40}]

PARI

a(n) = sum(k=1, n, binomial(n,k) * sigma(k, 2)); \\ Michel Marcus, Jul 24 2022

Formula

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

a(n) = Sum_{i=1..n} Sum_{j=1..n} (i^2)*binomial(n,i*j). - Ridouane Oudra, Oct 25 2022