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A280375 Expansion of Sum_{k>=1} k^3*x^(k^2)/(1 - x^k).

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%I A280375 #15 Jan 02 2017 20:34:41
%S A280375 1,1,1,9,1,9,1,9,28,9,1,36,1,9,28,73,1,36,1,73,28,9,1,100,126,9,28,73,
%T A280375 1,161,1,73,28,9,126,316,1,9,28,198,1,252,1,73,153,9,1,316,344,134,28,
%U A280375 73,1,252,126,416,28,9,1,441,1,9,371,585,126,252,1,73,28,477,1,828,1,9,153,73,344,252,1,710,757,9,1,659,126
%N A280375 Expansion of Sum_{k>=1} k^3*x^(k^2)/(1 - x^k).
%C A280375 The sum of the cubes of the divisors of n which are <= sqrt(n).
%H A280375 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A280375 G.f.: Sum_{k>=1} k^3*x^(k^2)/(1 - x^k).
%e A280375 The divisors of 12 which are <= sqrt(12) are {1,2,3}, so a(12) = 1^3 + 2^3 + 3^3 = 36.
%t A280375 nmax = 85; Rest[CoefficientList[Series[Sum[k^3 x^k^2/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
%t A280375 (* Second program *)
%t A280375 Table[Total[Select[Divisors@ n, # <= Sqrt@ n &]^3], {n, 85}] (* _Michael De Vlieger_, Jan 01 2017 *)
%o A280375 (PARI) a(n) = my(rn = sqrt(n)); sumdiv(n, d, d^3*(d<=rn)); \\ _Michel Marcus_, Jan 02 2017
%Y A280375 Cf. A001158, A038548, A066839, A095118.
%K A280375 nonn
%O A280375 1,4
%A A280375 _Ilya Gutkovskiy_, Jan 01 2017