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 A327626 Expansion of Sum_{k>=1} x^(k^3) / (1 - x^(k^3))^2. 2
 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, 28, 28, 29, 30, 31, 36, 33, 34, 35, 36, 37, 38, 39, 45, 41, 42, 43, 44, 45, 46, 47, 54, 49, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum of divisors d of n such that n/d is a cube. Inverse Moebius transform of A078429. LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 FORMULA a(n) = Sum_{d|n} A078429(d). a(n) = Sum_{d|n} A010057(n/d) * d. Dirichlet convolution of A000027 and A010057. D.g.f.: zeta(s-1)*zeta(3s). - R. J. Mathar, Jun 05 2020 Sum_{k=1..n} a(k) ~ Pi^6 * n^2 / 1890. - Vaclav Kotesovec, May 20 2021 MATHEMATICA 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 a[n_] := DivisorSum[n, # &, IntegerQ[(n/#)^(1/3)] &]; Table[a[n], {n, 1, 75}] PROG (PARI) A327626(n) = sumdiv(n, d, ispower(n/d, 3)*d); \\ Antti Karttunen, Sep 19 2019 CROSSREFS Cf. A000578, A004709 (fixed points), A010057, A061704, A076752, A078429, A113061. Sequence in context: A284049 A063932 A323785 * A179464 A071191 A300903 Adjacent sequences: A327623 A327624 A327625 * A327627 A327628 A327629 KEYWORD nonn,mult AUTHOR Ilya Gutkovskiy, Sep 19 2019 STATUS approved

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Last modified August 6 00:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)