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%I #13 Aug 30 2021 03:11:54
%S 1,2,3,4,5,6,7,16,17,18,19,20,21,22,23,32,33,34,35,36,37,38,39,48,49,
%T 50,78,79,80,81,82,91,92,93,94,95,96,97,98,107,108,109,110,111,112,
%U 113,114,123,124,125,126,127,128,156,157,166,167,168,169,170,171,172,173,246,247,248,249,250,251,252
%N a(n) = n + 2^3 * floor(n/2^3) + 3^3 * floor(n/3^3) + 4^3 * floor(n/4^3) + ...
%C Partial sums of A113061.
%H Seiichi Manyama, <a href="/A309126/b309126.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: (1/(1 - x)) * Sum_{k>=1} k^3 * x^(k^3)/(1 - x^(k^3)).
%F a(n) ~ zeta(4/3)*n^(4/3)/4 - n/2. - _Vaclav Kotesovec_, Aug 30 2021
%t Table[Sum[k^3 Floor[n/k^3], {k, 1, n}], {n, 1, 70}]
%t nmax = 70; CoefficientList[Series[1/(1 - x) Sum[k^3 x^(k^3)/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}], {x, 0, nmax}], x] // Rest
%o (PARI) a(n) = sum(k=1, n, k^3*(n\k^3)); \\ _Seiichi Manyama_, Aug 30 2021
%Y Cf. A013937, A024916, A113061, A309125, A309127.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Jul 13 2019
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