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 A078747 #17 Dec 30 2022 03:54:51
%S A078747 1,1,7,5,21,7,43,21,61,21,111,35,157,43,147,85,273,61,343,105,301,111,
%T A078747 507,147,521,157,547,215,813,147,931,341,777,273,903,305,1333,343,
%U A078747 1099,441,1641,301,1807,555,1281,507,2163,595,2101,521,1911,785,2757,547
%N A078747 Expansion of Sum_{k>0} k*phi(k)*x^k/(1+x^k).
%H A078747 Amiram Eldar, <a href="/A078747/b078747.txt">Table of n, a(n) for n = 1..10000</a>
%F A078747 Multiplicative with a(2^e) = (4^e-1)/3, a(p^e) = (p^(2*e+1)+1)/(p+1), p>2.
%F A078747 L.g.f.: log(Product_{k>=1} (1 + x^k)^phi(k)) = Sum_{n>=1} a(n)*x^n/n. - _Ilya Gutkovskiy_, May 21 2018
%F A078747 Sum_{k=1..n} a(k) ~ c * n^3, where c = zeta(3)/(4*zeta(2)) = 0.182690... (A240976). - _Amiram Eldar_, Oct 15 2022
%F A078747 Dirichlet g.f.: (zeta(s)*zeta(s-2)/zeta(s-1))*(1-2^(1-s)). - _Amiram Eldar_, Dec 30 2022
%t A078747 f[p_, e_] := If[p == 2, (4^e - 1)/3, (p^(2*e + 1) + 1)/(p + 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* _Amiram Eldar_, Oct 15 2022 *)
%o A078747 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,1] == 2, (4^f[i,2]-1)/3, (f[i,1]^(2*f[i,2]+1)+1)/(f[i,1]+1))); } \\ _Amiram Eldar_, Oct 15 2022
%Y A078747 Cf. A000010, A057660, A240976, A299069.
%K A078747 mult,nonn
%O A078747 1,3
%A A078747 _Vladeta Jovovic_, Dec 22 2002