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 A327626 #25 May 30 2025 01:09:54
%S A327626 1,2,3,4,5,6,7,9,9,10,11,12,13,14,15,18,17,18,19,20,21,22,23,27,25,26,
%T A327626 28,28,29,30,31,36,33,34,35,36,37,38,39,45,41,42,43,44,45,46,47,54,49,
%U A327626 50,51,52,53,56,55,63,57,58,59,60,61,62,63,73,65,66,67,68,69,70,71,81,73,74,75
%N A327626 Expansion of Sum_{k>=1} x^(k^3) / (1 - x^(k^3))^2.
%C A327626 Sum of divisors d of n such that n/d is a cube.
%C A327626 Inverse Moebius transform of A078429.
%H A327626 Antti Karttunen, <a href="/A327626/b327626.txt">Table of n, a(n) for n = 1..20000</a>
%F A327626 a(n) = Sum_{d|n} A078429(d).
%F A327626 a(n) = Sum_{d|n} A010057(n/d) * d. Dirichlet convolution of A000027 and A010057.
%F A327626 D.g.f.: zeta(s-1)*zeta(3s). - _R. J. Mathar_, Jun 05 2020
%F A327626 Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / 1890. - _Vaclav Kotesovec_, May 20 2021
%F A327626 Multiplicative with a(p^e) = (p^(e+3) - p^(e mod 3))/(p^3-1). - _Amiram Eldar_, May 25 2025
%t A327626 nmax = 75; CoefficientList[Series[Sum[x^(k^3)/(1 - x^(k^3))^2, {k, 1, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x] // Rest
%t A327626 a[n_] := DivisorSum[n, # &, IntegerQ[(n/#)^(1/3)] &]; Table[a[n], {n, 1, 75}]
%t A327626 f[p_, e_] := (p^(e+3) - p^Mod[e, 3])/(p^3-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, May 25 2025 *)
%o A327626 (PARI) A327626(n) = sumdiv(n,d,ispower(n/d,3)*d); \\ _Antti Karttunen_, Sep 19 2019
%Y A327626 Cf. A000578, A004709 (fixed points), A010057, A061704, A076752, A078429, A113061.
%K A327626 nonn,mult
%O A327626 1,2
%A A327626 _Ilya Gutkovskiy_, Sep 19 2019