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 A326125 #41 Jan 07 2023 04:03:36
%S A326125 1,2,12,4,30,24,56,8,117,60,132,48,182,112,360,16,306,234,380,120,672,
%T A326125 264,552,96,775,364,1080,224,870,720,992,32,1584,612,1680,468,1406,
%U A326125 760,2184,240,1722,1344,1892,528,3510,1104,2256,192,2793,1550,3672,728,2862,2160
%N A326125 Expansion of Sum_{k>=1} k^2 * x^k / (1 + x^k)^2.
%H A326125 Amiram Eldar, <a href="/A326125/b326125.txt">Table of n, a(n) for n = 1..10000</a>
%F A326125 G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^k * (1 + x^k) / (1 - x^k)^3.
%F A326125 a(n) = n * Sum_{d|n} (-1)^(n/d + 1) * d.
%F A326125 a(n) = n * A000593(n).
%F A326125 From _Amiram Eldar_, Dec 05 2022: (Start)
%F A326125 Multiplicative with a(2^e) = 2^e, and a(p^e) = p^e*(p^(e+1)-1)/(p-1) for p > 2.
%F A326125 Sum_{k=1..n} a(k) ~ c * n^3, where c = Pi^2/36 = 0.2741556... (A353908). (End)
%F A326125 Dirichlet g.f.: zeta(s-1)*zeta(s-2)*(1-2^(2-s)). - _Amiram Eldar_, Jan 07 2023
%t A326125 nmax = 54; CoefficientList[Series[Sum[k^2 x^k/(1 + x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A326125 Table[n Sum[(-1)^(n/d + 1) d, {d, Divisors[n]}], {n, 1, 54}]
%t A326125 f[p_, e_] := p^e*(p^(e+1)-1)/(p-1); f[2, e_] := 2^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Dec 05 2022 *)
%o A326125 (PARI) a(n)={n*sumdiv(n, d, (-1)^(n/d+1)*d)} \\ _Andrew Howroyd_, Sep 10 2019
%Y A326125 Cf. A000593, A064987, A078306, A143520, A185152, A245579, A326238, A353908.
%K A326125 nonn,mult
%O A326125 1,2
%A A326125 _Ilya Gutkovskiy_, Sep 10 2019