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%I #8 Dec 05 2021 05:57:22
%S 1,6,8,19,12,48,16,48,36,72,24,152,28,96,96,113,36,216,40,228,128,144,
%T 48,384,88,168,136,304,60,576,64,258,192,216,192,684,76,240,224,576,
%U 84,768,88,456,432,288,96,904,164,528,288,532,108,816,288,768,320,360,120,1824
%N a(n) = Sum_{d|n} usigma(d) * usigma(n/d).
%C Dirichlet convolution of A034448 with itself.
%F Dirichlet g.f.: ( zeta(s) * zeta(s-1) / zeta(2*s-1) )^2.
%F Multiplicative with a(p^e) = e * (p^e + 1) + (p+1) * (p^e - 1)/(p-1). - _Amiram Eldar_, Nov 29 2021
%F Sum_{k=1..n} a(k) ~ Pi^2 * n^2 / zeta(3)^2 * (Pi^2 * log(n)/72 + gamma * Pi^2/36 - Pi^2/144 + zeta'(2)/6 - Pi^2 * zeta'(3)/(18*zeta(3))), where zeta(3) = A002117, zeta'(2) = -A073002, zeta'(3) = -A244115 and gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Dec 05 2021
%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; a[n_] := Sum[usigma[d] usigma[n/d], {d, Divisors[n]}]; Table[a[n], {n, 1, 60}]
%Y Cf. A034448, A034761, A322328, A328485, A343569.
%K nonn,mult
%O 1,2
%A _Ilya Gutkovskiy_, Nov 29 2021
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