A386780 a(n) = n^3*sigma_6(n).

0, 1, 520, 19710, 266304, 1953250, 10249200, 40353950, 136348160, 387952659, 1015690000, 2357949022, 5248851840, 10604501570, 20984054000, 38498557500, 69810262016, 118587881410, 201735382680, 322687704638, 520158288000, 795376354500, 1226133491440, 1801152673630

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. A282211, A386746, A282213, A386748, A282781, A386781, A386782.

Cf. A013954, A386750, A386777.

Programs

Magma

[0] cat [n^3*DivisorSigma(6, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025

Mathematica

Table[n^3*DivisorSigma[6, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^9*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Sum_{k>=1} k^9*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4.

a(n) = n^3*A013954(n).

Dirichlet g.f.: zeta(s-3)*zeta(s-9). - R. J. Mathar, Aug 03 2025