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 A386783 #19 Aug 04 2025 02:28:32
%S A386783 0,1,80,810,5376,16250,64800,120050,348160,597051,1300000,1786202,
%T A386783 4354560,4855370,9604000,13162500,22347776,24221090,47764080,47176202,
%U A386783 87360000,97240500,142896160,148315730,282009600,254296875,388429600,435781620,645388800,595530602,1053000000
%N A386783 a(n) = n^4*sigma_2(n).
%H A386783 Vincenzo Librandi, <a href="/A386783/b386783.txt">Table of n, a(n) for n = 0..10000</a>
%F A386783 G.f.: Sum_{k>=1} k^4*x^k*(1 + 57*x^k + 302*x^(2*k) + 302*x^(3*k) + 57*x^(4*k) + x^(5*k)) / (1 - x^k)^7.
%F A386783 a(n) = n^4*A001157(n).
%F A386783 Dirichlet g.f.: zeta(s-4)*zeta(s-6). - _R. J. Mathar_, Aug 03 2025
%t A386783 Table[n^4*DivisorSigma[2, n], {n, 0, 40}]
%t A386783 nmax = 40; CoefficientList[Series[Sum[k^4*x^k*(1 + 57*x^k + 302*x^(2*k) + 302*x^(3*k) + 57*x^(4*k) + x^(5*k)) / (1 - x^k)^7, {k, 1, nmax}], {x, 0, nmax}], x]
%o A386783 (Magma) [0] cat [n^4*DivisorSigma(2, n): n in [1..35]]; // _Vincenzo Librandi_, Aug 03 2025
%Y A386783 Cf. A280022, A280025, A386784, A386785, A386786, A386787, A386788.
%Y A386783 Cf. A001157, A328259, A386745, A386746.
%K A386783 nonn,mult
%O A386783 0,3
%A A386783 _Vaclav Kotesovec_, Aug 02 2025