A386751 a(n) = n*sigma_8(n).
0, 1, 514, 19686, 263172, 1953130, 10118604, 40353614, 134744072, 387479547, 1003908820, 2357947702, 5180803992, 10604499386, 20741757596, 38449317180, 68988964880, 118587876514, 199164487158, 322687697798, 514009128360, 794401245204, 1211985118828, 1801152661486
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Programs
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Magma
[0] cat [n*DivisorSigma(8,n): n in [1..25]]; // Vincenzo Librandi, Aug 02 2025
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Mathematica
Table[n*DivisorSigma[8, n], {n, 0, 40}] nmax = 40; CoefficientList[Series[x*Sum[k^9*x^(k-1)/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Sum_{k>=1} k^9*x^(k-1)/(1 - x^k)^2.
a(n) = n*A013956(n).
Dirichlet g.f.: zeta(s-1)*zeta(s-9). - R. J. Mathar, Aug 03 2025