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 A386787 #19 Aug 03 2025 12:36:49
%S A386787 0,1,2064,177228,4227328,48828750,365798592,1977329144,8657571840,
%T A386787 31395415077,100782540000,285311685252,749200886784,1792160422598,
%U A386787 4081207353216,8653821705000,17730707193856,34271896391154,64800136718928,116490259028540,206415142080000,350438089532832
%N A386787 a(n) = n^4*sigma_7(n).
%H A386787 Vincenzo Librandi, <a href="/A386787/b386787.txt">Table of n, a(n) for n = 0..7500</a>
%F A386787 G.f.: Sum_{k>=1} k^4*x^k*(1 + 2036*x^k + 152637*x^(2*k) + 2203488*x^(3*k) + 9738114*x^(4*k) + 15724248*x^(5*k) + 9738114*x^(6*k) + 2203488*x^(7*k) + 152637*x^(8*k) + 2036*x^(9*k) + x^(10*k))/(1 - x^k)^12.
%F A386787 a(n) = (33*A386815(n) + 110*A386816(n) + 13*A282012(n) - 132*A386817(n) - 132*A282596(n) + 88*A386818(n) + 20*A282287(n))/41472.
%F A386787 a(n) = n^4*A013955(n).
%F A386787 Dirichlet g.f.: zeta(s-4)*zeta(s-11). - _R. J. Mathar_, Aug 03 2025
%t A386787 Table[n^4*DivisorSigma[7, n], {n, 0, 30}]
%t A386787 (* or *)
%t A386787 nmax = 30; CoefficientList[Series[Sum[k^4*x^k*(1 + 2036*x^k + 152637*x^(2*k) + 2203488*x^(3*k) + 9738114*x^(4*k) + 15724248*x^(5*k) + 9738114*x^(6*k) + 2203488*x^(7*k) + 152637*x^(8*k) + 2036*x^(9*k) + x^(10*k))/(1 - x^k)^12, {k, 1, nmax}], {x, 0, nmax}], x]
%t A386787 (* or *)
%t A386787 terms = 30; E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}]; E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}]; E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}]; CoefficientList[Series[(33*E2[x]^4*E4[x]^2 + 110*E2[x]^2*E4[x]^3 + 13*E4[x]^4 - 132*E2[x]^3*E4[x]*E6[x] - 132*E2[x]*E4[x]^2*E6[x] + 88*E2[x]^2*E6[x]^2 + 20*E4[x]*E6[x]^2)/41472, {x, 0, terms}], x]
%o A386787 (Magma) [0] cat [n^4*DivisorSigma(7, n): n in [1..35]]; // _Vincenzo Librandi_, Aug 03 2025
%Y A386787 Cf. A280022, A386783, A280025, A386784, A386785, A386786, A386788.
%Y A386787 Cf. A013955, A282060, A282753, A386781.
%Y A386787 Cf. A386815, A386816, A282012, A386817, A282596, A386818, A282287.
%K A386787 nonn,mult
%O A386787 0,3
%A A386787 _Vaclav Kotesovec_, Aug 02 2025