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%I #18 May 20 2021 09:26:48
%S 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 28,28,29,30,31,36,33,34,35,36,37,38,39,45,41,42,43,44,45,46,47,54,49,
%U 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 Expansion of Sum_{k>=1} x^(k^3) / (1 - x^(k^3))^2.
%C Sum of divisors d of n such that n/d is a cube.
%C Inverse Moebius transform of A078429.
%H Antti Karttunen, <a href="/A327626/b327626.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = Sum_{d|n} A078429(d).
%F a(n) = Sum_{d|n} A010057(n/d) * d. Dirichlet convolution of A000027 and A010057.
%F D.g.f.: zeta(s-1)*zeta(3s). - _R. J. Mathar_, Jun 05 2020
%F Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / 1890. - _Vaclav Kotesovec_, May 20 2021
%t 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 a[n_] := DivisorSum[n, # &, IntegerQ[(n/#)^(1/3)] &]; Table[a[n], {n, 1, 75}]
%o (PARI) A327626(n) = sumdiv(n,d,ispower(n/d,3)*d); \\ _Antti Karttunen_, Sep 19 2019
%Y Cf. A000578, A004709 (fixed points), A010057, A061704, A076752, A078429, A113061.
%K nonn,mult
%O 1,2
%A _Ilya Gutkovskiy_, Sep 19 2019
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