This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309126 #13 Aug 30 2021 03:11:54 %S A309126 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 A309126 50,78,79,80,81,82,91,92,93,94,95,96,97,98,107,108,109,110,111,112, %U A309126 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 A309126 a(n) = n + 2^3 * floor(n/2^3) + 3^3 * floor(n/3^3) + 4^3 * floor(n/4^3) + ... %C A309126 Partial sums of A113061. %H A309126 Seiichi Manyama, <a href="/A309126/b309126.txt">Table of n, a(n) for n = 1..10000</a> %F A309126 G.f.: (1/(1 - x)) * Sum_{k>=1} k^3 * x^(k^3)/(1 - x^(k^3)). %F A309126 a(n) ~ zeta(4/3)*n^(4/3)/4 - n/2. - _Vaclav Kotesovec_, Aug 30 2021 %t A309126 Table[Sum[k^3 Floor[n/k^3], {k, 1, n}], {n, 1, 70}] %t A309126 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 A309126 (PARI) a(n) = sum(k=1, n, k^3*(n\k^3)); \\ _Seiichi Manyama_, Aug 30 2021 %Y A309126 Cf. A013937, A024916, A113061, A309125, A309127. %K A309126 nonn %O A309126 1,2 %A A309126 _Ilya Gutkovskiy_, Jul 13 2019