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 A360908 #20 Mar 25 2025 08:57:15
%S A360908 1,1,1,3,1,1,1,5,3,1,1,3,1,1,1,7,1,3,1,3,1,1,1,5,3,1,5,3,1,1,1,9,1,1,
%T A360908 1,9,1,1,1,5,1,1,1,3,3,1,1,7,3,3,1,3,1,5,1,5,1,1,1,3,1,1,3,11,1,1,1,3,
%U A360908 1,1,1,15,1,1,3,3,1,1,1,7,7,1,1,3,1,1
%N A360908 Multiplicative with a(p^e) = 2*e - 1.
%H A360908 Vaclav Kotesovec, <a href="/A360908/b360908.txt">Table of n, a(n) for n = 1..10000</a>
%F A360908 Dirichlet g.f.: zeta(s) * Product_{p prime} (1 + 2/(p^s*(p^s-1))).
%F A360908 Sum_{k=1..n} a(k) ~ c*n, where c = A367822 = Product_{p prime} (1 + 2/(p*(p-1))) = 3.279577150984783607372919498914633983999130708105267540952619534539808381...
%F A360908 a(n) = A361430(n^2). - _Amiram Eldar_, Feb 11 2024
%t A360908 a[n_] := Times @@ ((2*Last[#] - 1) & /@ FactorInteger[n]); a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Feb 25 2023 *)
%o A360908 (PARI) for(n=1, 100, print1(direuler(p=2, n, (1+(1+1/X)/(1-1/X)^2))[n], ", "))
%o A360908 (PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k,1]=2*f[k,2]-1; f[k,2]=1); factorback(f); \\ _Michel Marcus_, Feb 25 2023
%Y A360908 Cf. A048691, A322327, A361430, A367822.
%K A360908 nonn,mult
%O A360908 1,4
%A A360908 _Vaclav Kotesovec_, Feb 25 2023