A386748 a(n) = n^3*sigma_4(n).

0, 1, 136, 2214, 17472, 78250, 301104, 823886, 2236928, 4842747, 10642000, 19488502, 38683008, 62750714, 112048496, 173245500, 286330880, 410343586, 658613592, 893878598, 1367184000, 1824083604, 2650436272, 3404837614, 4952558592, 6113296875, 8534097104, 10591107372

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..8000

Formula

G.f.: Sum_{k>=1} k^7*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4. - Amiram Eldar, Aug 01 2025

a(n) = n^3*A001159(n).

Dirichlet g.f.: zeta(s-3)*zeta(s-7). - R. J. Mathar, Aug 03 2025

Sum_{k=0..n} a(k) ~ zeta(5) * n^8 / 8. - Amiram Eldar, Nov 11 2025

Mathematica

Table[n^3*DivisorSigma[4, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^7*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(Magma) [0] cat [n^3*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 02 2025

Crossrefs

Cf. A000578, A001159, A013663, A386749, A386747.

Sequence in context: A235190 A249985 A072897 * A254703 A333110 A250424

Adjacent sequences: A386745 A386746 A386747 * A386749 A386750 A386751

Keyword

nonn,mult,easy

Author

Vaclav Kotesovec, Aug 01 2025

Status

approved