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 A340850 #10 Oct 16 2022 08:00:04
%S A340850 1,1,4,5,16,4,36,21,40,16,100,20,144,36,64,85,256,40,324,80,144,100,
%T A340850 484,84,416,144,364,180,784,64,900,341,400,256,576,200,1296,324,576,
%U A340850 336,1600,144,1764,500,640,484,2116,340,1800,416,1024,720,2704,364,1600,756,1296,784
%N A340850 Dirichlet g.f.: Sum_{n>0} a(n)/n^s = zeta(s) * zeta(s-2) / (zeta(s-1))^2.
%F A340850 Multiplicative with a(1) = 1 and a(p^e) = (p^(2*e)-1) * (p-1) / (p+1) for prime p and e > 0.
%F A340850 Dirichlet convolution of A002618 and A023900.
%F A340850 Dirichlet convolution of A001157 and A328722.
%F A340850 Dirichlet inverse b(n) for n > 0 is multiplicative with b(1) = 1 and b(p^e) = -(p-1)^2 * e * p^(e-1) for prime p and e > 0.
%F A340850 Dirichlet convolution with A060640 equals A007433.
%F A340850 Dirichlet convolution with A018804 equals A000290.
%F A340850 Sum_{k=1..n} a(k) ~ c * n^3, where c = 12*zeta(3)/Pi^4 = 0.148083... . - _Amiram Eldar_, Oct 16 2022
%t A340850 f[p_, e_] := (p^(2*e) - 1)*(p - 1)/(p + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 24 2021 *)
%Y A340850 Cf. A000290, A001157, A002618, A007433, A018804, A023900, A060640, A328722.
%K A340850 nonn,easy,mult
%O A340850 1,3
%A A340850 _Werner Schulte_, Jan 24 2021