A386782 a(n) = n^3*sigma_8(n).

0, 1, 2056, 177174, 4210752, 48828250, 364269744, 1977327086, 8623620608, 31385843307, 100390882000, 285311671942, 746035774848, 1792160396234, 4065384488816, 8651096365500, 17661175009280, 34271896312546, 64529293839192, 116490258905078, 205603651344000, 350330949134964

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, A386780, A386781.

Cf. A013956, A386751, A386778.

Programs

Magma

[0] cat [n^3*DivisorSigma(8, n): n in [1..35]]; // Vincenzo Librandi, Aug 04 2025

Mathematica

Table[n^3*DivisorSigma[8, n], {n, 0, 30}]
nmax = 30; CoefficientList[Series[Sum[k^11*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^11*x^k*(x^(2*k) + 4*x^k + 1)/(1 - x^k)^4.

a(n) = n^3*A013956(n).

Dirichlet g.f.: zeta(s-3)*zeta(s-11). - R. J. Mathar, Aug 03 2025