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 A328705 #13 Nov 30 2020 04:01:09 %S A328705 1,2,2,5,2,4,2,10,5,4,2,10,2,4,4,20,2,10,2,10,4,4,2,20,5,4,10,10,2,8, %T A328705 2,36,4,4,4,25,2,4,4,20,2,8,2,10,10,4,2,40,5,10,4,10,2,20,4,20,4,4,2, %U A328705 20,2,4,10,65,4,8,2,10,4,8,2,50,2,4,10,10,4,8,2,40 %N A328705 Dirichlet g.f.: Product_{k>=1} zeta(k*s)^2. %C A328705 Dirichlet convolution of A000688 with itself. %H A328705 Vaclav Kotesovec, <a href="/A328705/b328705.txt">Table of n, a(n) for n = 1..10000</a> %F A328705 a(n) = Sum_{d|n} A000688(n/d) * A000688(d). %F A328705 Sum_{k=1..n} a(k) ~ c^2 * n * (log(n) + 2*gamma - 1 - 2*s), where c = A021002 = Product_{k>=2} zeta(k) = 2.2948565916733137941835158313443112887131637994..., s = Sum_{k>=2} k*zeta'(k)/zeta(k) = -2.1955691982567064617939038695473479681910375... and gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Oct 26 2019 %F A328705 Multiplicative with a(p^e) = A000712(e). - _Amiram Eldar_, Nov 30 2020 %t A328705 Table[DivisorSum[n, FiniteAbelianGroupCount[n/#] FiniteAbelianGroupCount[#] &], {n, 1, 80}] %Y A328705 Cf. A000688, A000712, A001620, A063966, A129667, A188581, A188585, A301830. %K A328705 nonn,mult %O A328705 1,2 %A A328705 _Ilya Gutkovskiy_, Oct 26 2019