This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386788 #20 Aug 03 2025 10:21:25
%S A386788 0,1,4112,531522,16843008,244141250,2185618464,13841289602,
%T A386788 68988964864,282472589763,1003908820000,3138428391362,8952429298176,
%U A386788 23298085151042,56915382843424,129766445482500,282578800148480,582622237313282,1161527289105456,2213314919196482,4112073026880000
%N A386788 a(n) = n^4*sigma_8(n).
%H A386788 Vaclav Kotesovec, <a href="/A386788/b386788.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..7500 from Vincenzo Librandi)
%F A386788 G.f.: Sum_{k>=1} k^4*x^k*(1 + 4083*x^k + 478271*x^(2*k) + 10187685*x^(3*k) + 66318474*x^(4*k) + 162512286*x^(5*k) + 162512286*x^(6*k) + 66318474*x^(7*k) + 10187685*x^(8*k) + 478271*x^(9*k) + 4083*x^(10*k) + x^(11*k))/(1 - x^k)^13.
%F A386788 a(n) = n^4*A013956(n).
%F A386788 Dirichlet g.f.: zeta(s-4)*zeta(s-12). - _R. J. Mathar_, Aug 03 2025
%t A386788 Table[n^4*DivisorSigma[8, n], {n, 0, 30}]
%t A386788 nmax = 30; CoefficientList[Series[Sum[k^4*x^k*(1 + 4083*x^k + 478271*x^(2*k) + 10187685*x^(3*k) + 66318474*x^(4*k) + 162512286*x^(5*k) + 162512286*x^(6*k) + 66318474*x^(7*k) + 10187685*x^(8*k) + 478271*x^(9*k) + 4083*x^(10*k) + x^(11*k))/(1 - x^k)^13, {k, 1, nmax}], {x, 0, nmax}], x]
%o A386788 (Magma) [0] cat [n^4*DivisorSigma(8, n): n in [1..35]]; // _Vincenzo Librandi_, Aug 03 2025
%o A386788 (PARI) a(n) = if (n, n^4*sigma(n,8), 0); \\ _Michel Marcus_, Aug 03 2025
%Y A386788 Cf. A280022, A386783, A280025, A386784, A386785, A386786, A386787.
%Y A386788 Cf. A013956, A386751, A386778, A386782.
%K A386788 nonn,mult
%O A386788 0,3
%A A386788 _Vaclav Kotesovec_, Aug 02 2025