A386784 a(n) = n^4*sigma_4(n).

0, 1, 272, 6642, 69888, 391250, 1806624, 5767202, 17895424, 43584723, 106420000, 214373522, 464196096, 815759282, 1568678944, 2598682500, 4581294080, 6975840962, 11855044656, 16983693362, 27343680000, 38305755684, 58309597984, 78311265122, 118861406208, 152832421875

Offset: 0

Author

Vaclav Kotesovec, Aug 02 2025

Keywords

• nonn
• mult

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A280022, A386783, A280025, A386785, A386786, A386787, A386788.

Cf. A001159, A386749, A386747, A386748.

Programs

Magma

[0] cat [n^4*DivisorSigma(4, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025

Mathematica

Table[n^4*DivisorSigma[4, n], {n, 0, 40}]
nmax = 40; CoefficientList[Series[Sum[k^4*x^k*(1 + 247*x^k + 4293*x^(2*k) + 15619*x^(3*k) + 15619*x^(4*k) + 4293*x^(5*k) + 247*x^(6*k) + x^(7*k))/(1 - x^k)^9, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^4*x^k*(1 + 247*x^k + 4293*x^(2*k) + 15619*x^(3*k) + 15619*x^(4*k) + 4293*x^(5*k) + 247*x^(6*k) + x^(7*k))/(1 - x^k)^9.

a(n) = n^4*A001159(n).

Dirichlet g.f.: zeta(s-4)*zeta(s-8). - R. J. Mathar, Aug 03 2025