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G.f.: Sum_{k>=1} k^3 * x^(k*(k + 1)) / (1 - x^k).
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%I #8 Dec 02 2020 03:19:01

%S 0,1,1,1,1,9,1,9,1,9,1,36,1,9,28,9,1,36,1,73,28,9,1,100,1,9,28,73,1,

%T 161,1,73,28,9,126,100,1,9,28,198,1,252,1,73,153,9,1,316,1,134,28,73,

%U 1,252,126,416,28,9,1,441,1,9,371,73,126,252,1,73,28,477,1,828,1,9,153,73,344

%N G.f.: Sum_{k>=1} k^3 * x^(k*(k + 1)) / (1 - x^k).

%C Sum of cubes of divisors of n that are smaller than sqrt(n).

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>

%t nmax = 77; CoefficientList[Series[Sum[k^3 x^(k (k + 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

%t Table[DivisorSum[n, #^3 &, # < Sqrt[n] &], {n, 77}]

%o (PARI) a(n) = sumdiv(n, d, if (d^2 < n, d^3)); \\ _Michel Marcus_, Dec 02 2020

%Y Cf. A001158, A056924, A070039, A276634, A280375, A339353.

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Dec 01 2020