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 A328485 #14 Feb 10 2023 11:53:00
%S A328485 1,4,5,9,7,20,9,18,15,28,13,45,15,36,35,35,19,60,21,63,45,52,25,90,33,
%T A328485 60,43,81,31,140,33,68,65,76,63,135,39,84,75,126,43,180,45,117,105,
%U A328485 100,49,175,59,132,95,135,55,172,91,162,105,124,61,315,63,132,135,133,105
%N A328485 Dirichlet g.f.: zeta(s)^2 * zeta(s-1) / zeta(2*s-1).
%C A328485 Inverse Moebius transform of A034448.
%C A328485 Dirichlet convolution of A055615 with A064840.
%H A328485 Amiram Eldar, <a href="/A328485/b328485.txt">Table of n, a(n) for n = 1..10000</a>
%F A328485 G.f.: Sum_{k>=1} usigma(k) * x^k / (1 - x^k), where usigma = A034448.
%F A328485 a(n) = Sum_{d|n} usigma(d).
%F A328485 a(n) = n * Sum_{d|n} mu(n/d) * tau(d) * sigma(d) / d, where mu = A008683, tau = A000005 and sigma = A000203.
%F A328485 Sum_{k=1..n} a(k) ~ Pi^4 * n^2 / (72 * zeta(3)). - _Vaclav Kotesovec_, Oct 17 2019
%F A328485 From _Amiram Eldar_, Feb 10 2023: (Start)
%F A328485 a(n) = Sum_{d|n} Sum_{d'|n, gcd(d, d')=1} d'.
%F A328485 Multiplicative with a(p^e) = (p^(e+1)-p)/(p-1) + e + 1. (End)
%p A328485 with(numtheory):
%p A328485 a:= n-> add(mobius(d)*tau(n/d)*sigma(n/d)*d, d=divisors(n)):
%p A328485 seq(a(n), n=1..70); # _Alois P. Heinz_, Oct 16 2019
%t A328485 Table[n DivisorSum[n, MoebiusMu[n/#] DivisorSigma[0, #] DivisorSigma[1, #]/# &], {n, 1, 65}]
%t A328485 nmax = 65; CoefficientList[Series[Sum[DivisorSum[k, # &, CoprimeQ[#, k/#] &] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A328485 f[p_, e_] := (p^(e + 1) - p)/(p - 1) + e + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 10 2023 *)
%o A328485 (PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); prod(i = 1, #p, (p[i]^(e[i] + 1) - p[i])/(p[i] - 1) + e[i] + 1);} \\ _Amiram Eldar_, Feb 10 2023
%Y A328485 Cf. A000005, A000203, A007429, A008683, A034448, A048691, A055615, A064840, A319131, A319132.
%K A328485 nonn,mult
%O A328485 1,2
%A A328485 _Ilya Gutkovskiy_, Oct 16 2019