A356039 a(n) = Sum_{k=1..n} binomial(n,k) * sigma_3(k).

1, 11, 58, 243, 866, 2804, 8485, 24387, 67333, 180086, 469338, 1196976, 2996956, 7385837, 17954243, 43125267, 102494548, 241309031, 563341508, 1305142418, 3002938045, 6866090880, 15609292379, 35299794600, 79443050541, 177989130174, 397124963671, 882642816697, 1954708794400

Offset

1,2

Comments

For m>0, Sum_{k=1..n} binomial(n,k) * sigma_m(k) ~ zeta(m+1) * n^m * 2^(n-m).

Links

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Divisor Function.

Formula

a(n) ~ Pi^4 * n^3 * 2^(n-4) / 45.

a(n) = Sum_{i=1..n} Sum_{j=1..n} (i^3)*binomial(n,i*j). - Ridouane Oudra, Oct 31 2022

Maple

with(numtheory): seq(add(sigma[3](i)*binomial(n, i), i=1..n), n=1..60); # Ridouane Oudra, Oct 31 2022

Mathematica

Table[Sum[Binomial[n, k] * DivisorSigma[3, k], {k, 1, n}], {n, 1, 40}]

Prog

(PARI) a(n) = sum(k=1, n, binomial(n, k) * sigma(k, 3)); \\ Michel Marcus, Jul 24 2022

Crossrefs

Cf. A001158, A160399, A185003, A356038.

Cf. A006218, A024916, A064602, A064603.

Sequence in context: A256226 A290360 A359719 * A073720 A257364 A141302

Adjacent sequences: A356036 A356037 A356038 * A356040 A356041 A356042

Keyword

nonn

Author

Vaclav Kotesovec, Jul 24 2022

Status

approved