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%I #20 Sep 05 2021 07:39:09
%S 1,2,3,4,5,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,
%T 36,38,40,41,44,45,47,49,51,52,55,56,58,60,62,63,66,67,69,71,73,74,77,
%U 78,80,82,84,85,88,89,91,93,95,96,99,100,102,104,107,108,111,112,115,117,119,120,124,125,127,129,132,133,136
%N Partial sums of A347516.
%H Seiichi Manyama, <a href="/A347517/b347517.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: (1/(1 - x)) * Sum_{k>=1} x^(k^3)/(1 - x^k).
%t f[n_] := DivisorSum[n, 1 &, # <= n^(1/3) &]; Accumulate @ Array[f, 100] (* _Amiram Eldar_, Sep 04 2021 *)
%o (PARI) N=99; x='x+O('x^N); Vec(sum(k=1, N^(1/3), x^k^3/(1-x^k))/(1-x))
%o (PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^3<=k)); \\ _Michel Marcus_, Sep 05 2021
%Y Cf. A006218, A048766, A094820, A347516.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Sep 04 2021
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