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 A356536 #20 Feb 27 2023 16:49:22 %S A356536 1,82,866,6195,22071,85575,203911,546136,1119185,2405141,4179365, %T A356536 8357301,13188505,22773721,35220505,57132266,81279662,127696631, %U A356536 174756231,259359435,352134859,495847003,643907227,912211627,1160305628,1551633152,1969426752,2600039296 %N A356536 a(n) = Sum_{k=1..n} sigma_3(k)^2. %C A356536 Partial sums of A356534. %C A356536 In general, for m>0, Sum_{k=1..n} sigma_m(k)^2 ~ zeta(2*m+1) * zeta(m+1)^2 * n^(2*m+1) / ((2*m+1) * zeta(2*m+2)). %H A356536 Amiram Eldar, <a href="/A356536/b356536.txt">Table of n, a(n) for n = 1..10000</a> %F A356536 a(n) ~ zeta(7) * n^7 / 6. %t A356536 Table[Sum[DivisorSigma[3, k]^2, {k, 1, n}], {n, 1, 40}] %t A356536 Accumulate[DivisorSigma[3,Range[40]]^2] (* This program is much more efficient than the first program above. *) (* _Harvey P. Dale_, Feb 27 2023 *) %o A356536 (PARI) a(n) = sum(k=1, n, sigma(k, 3)^2); \\ _Michel Marcus_, Aug 11 2022 %Y A356536 Cf. A001158, A057434, A061502, A072379, A356535. %Y A356536 Cf. A127473, A035116, A072861, A356533, A356534. %K A356536 nonn %O A356536 1,2 %A A356536 _Vaclav Kotesovec_, Aug 11 2022