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 A318742 #33 Sep 04 2024 12:25:12
%S A318742 1,9,29,74,136,254,382,596,833,1173,1505,2057,2527,3209,3921,4856,
%T A318742 5674,6928,7956,9474,10882,12608,14128,16506,18369,20797,23141,26129,
%U A318742 28567,32259,35051,38963,42483,46675,50435,55904,59902,65156,70092,76460
%N A318742 a(n) = Sum_{k=1..n} floor(n/k)^3.
%H A318742 Seiichi Manyama, <a href="/A318742/b318742.txt">Table of n, a(n) for n = 1..10000</a>
%H A318742 Richard J. Mathar, <a href="https://arxiv.org/abs/2408.15212">Chebyshev approximation of x^m (-log x)^l in the interval 0 <= x <= 1</a>, arXiv:2408.15212 [math.CA], 2024. See p. 2.
%F A318742 a(n) = A006218(n) - 3*A024916(n) + 3*A064602(n).
%F A318742 a(n) ~ zeta(3) * n^3.
%F A318742 G.f.: (1/(1 - x)) * Sum_{k>=1} (3*k*(k - 1) + 1) * x^k/(1 - x^k). - _Ilya Gutkovskiy_, Jul 16 2019
%t A318742 Table[Sum[Floor[n/k]^3, {k, 1, n}], {n, 1, 40}]
%t A318742 Accumulate[Table[DivisorSigma[0, k] - 3*DivisorSigma[1, k] + 3*DivisorSigma[2, k], {k, 1, 40}]]
%o A318742 (PARI) a(n) = sum(k=1, n, (n\k)^3); \\ _Michel Marcus_, Sep 03 2018
%o A318742 (Magma) [&+[Floor(n/k)^3:k in [1..n]]: n in [1..40]]; // _Marius A. Burtea_, Jul 16 2019
%o A318742 (Python)
%o A318742 from math import isqrt
%o A318742 def A318742(n): return -(s:=isqrt(n))**4 + sum((q:=n//k)*(3*k*(k-1)+q**2+1) for k in range(1,s+1)) # _Chai Wah Wu_, Oct 21 2023
%Y A318742 Cf. A000005, A000203, A024916, A064602, A064603, A064604.
%Y A318742 Cf. A006218, A222548, A318743, A318744.
%K A318742 nonn
%O A318742 1,2
%A A318742 _Vaclav Kotesovec_, Sep 02 2018