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 A320941 #18 Jan 03 2025 05:18:24
%S A320941 1,6,15,36,56,111,141,240,300,446,507,791,820,1161,1310,1736,1786,
%T A320941 2505,2471,3346,3466,4307,4325,5895,5581,7026,7230,8905,8556,11246,
%U A320941 10417,13176,13050,15476,15106,19391,17576,21495,21374,25690,23822,30162,27435,33707,32990,37841,35721
%N A320941 Expansion of Sum_{k>=1} x^k*(1 + x^k)/(1 - x^k)^4.
%C A320941 Inverse Möbius transform of square pyramidal numbers (A000330).
%H A320941 Amiram Eldar, <a href="/A320941/b320941.txt">Table of n, a(n) for n = 1..10000</a>
%H A320941 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%F A320941 G.f.: Sum_{k>=1} A000330(k)*x^k/(1 - x^k).
%F A320941 a(n) = Sum_{d|n} d*(d + 1)*(2*d + 1)/6.
%F A320941 a(n) = (A000203(n) + 3*A001157(n) + 2*A001158(n))/6.
%F A320941 a(n) = Sum_{i=1..n} i^2*A135539(n,i). - _Ridouane Oudra_, Jul 22 2022
%F A320941 From _Amiram Eldar_, Jan 03 2025: (Start)
%F A320941 Dirichlet g.f.: zeta(s) * (2*zeta(s-3) + 3*zeta(s-2) + zeta(s-1)) / 6.
%F A320941 Sum_{k=1..n} a(k) ~ (zeta(4)/12) * n^4. (End)
%p A320941 a:=series(add(x^k*(1+x^k)/(1-x^k)^4,k=1..100),x=0,48): seq(coeff(a,x,n),n=1..47); # _Paolo P. Lava_, Apr 02 2019
%t A320941 nmax = 47; Rest[CoefficientList[Series[Sum[x^k (1 + x^k)/(1 - x^k)^4, {k, 1, nmax}], {x, 0, nmax}], x]]
%t A320941 Table[Sum[d (d + 1) (2 d + 1)/6, {d, Divisors[n]}], {n, 47}]
%t A320941 Table[(DivisorSigma[1, n] + 3 DivisorSigma[2, n] + 2 DivisorSigma[3, n])/6, {n, 47}]
%o A320941 (PARI) a(n) = my(f = factor(n)); (2*sigma(f, 3) + 3*sigma(f, 2) + sigma(f, 1)) / 6; \\ _Amiram Eldar_, Jan 03 2025
%Y A320941 Cf. A000203, A000330, A001157, A001158, A007437, A059358.
%Y A320941 Cf. A135539.
%K A320941 nonn,easy
%O A320941 1,2
%A A320941 _Ilya Gutkovskiy_, Oct 24 2018