A386786 a(n) = n^4*sigma_6(n).
0, 1, 1040, 59130, 1065216, 9766250, 61495200, 282477650, 1090785280, 3491573931, 10156900000, 25937439242, 62986222080, 137858520410, 293776756000, 577478362500, 1116964192256, 2015993983970, 3631236888240, 6131066388122, 10403165760000, 16702903444500, 26974936811680
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Crossrefs
Programs
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Magma
[0] cat [n^4*DivisorSigma(6, n): n in [1..35]]; // Vincenzo Librandi, Aug 03 2025
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Mathematica
Table[n^4*DivisorSigma[6, n], {n, 0, 30}] nmax = 30; CoefficientList[Series[Sum[k^4*x^k*(1 + 1013*x^k + 47840*x^(2*k) + 455192*x^(3*k) + 1310354*x^(4*k) + 1310354*x^(5*k) + 455192*x^(6*k) + 47840*x^(7*k) + 1013*x^(8*k) + x^(9*k))/(1 - x^k)^11, {k, 1, nmax}], {x, 0, nmax}], x]
Formula
G.f.: Sum_{k>=1} k^4*x^k*(1 + 1013*x^k + 47840*x^(2*k) + 455192*x^(3*k) + 1310354*x^(4*k) + 1310354*x^(5*k) + 455192*x^(6*k) + 47840*x^(7*k) + 1013*x^(8*k) + x^(9*k))/(1 - x^k)^11.
a(n) = n^4*A013954(n).
Dirichlet g.f.: zeta(s-4)*zeta(s-10). - R. J. Mathar, Aug 03 2025