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 A360911 #11 Feb 25 2023 12:14:14 %S A360911 1,1,1,4,1,1,1,7,4,1,1,4,1,1,1,10,1,4,1,4,1,1,1,7,4,1,7,4,1,1,1,13,1, %T A360911 1,1,16,1,1,1,7,1,1,1,4,4,1,1,10,4,4,1,4,1,7,1,7,1,1,1,4,1,1,4,16,1,1, %U A360911 1,4,1,1,1,28,1,1,4,4,1,1,1,10,10,1,1,4 %N A360911 Multiplicative with a(p^e) = 3*e - 2. %H A360911 Vaclav Kotesovec, <a href="/A360911/b360911.txt">Table of n, a(n) for n = 1..10000</a> %F A360911 Dirichlet g.f.: zeta(s)^2 * Product_{primes p} (1 - 1/p^s + 3/p^(2*s)). %F A360911 Dirichlet g.f.: zeta(s) * Product_{primes p} (1 + 3/(p^s*(p^s-1))). %F A360911 Sum_{k=1..n} a(k) ~ c*n, where c = Product_{primes p} (1 + 3/(p*(p-1))) = 5.092999766083306437144607885642959667401184716827970969797879646796872425... %t A360911 a[n_] := Times @@ ((3*Last[#] - 2) & /@ FactorInteger[n]); a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Feb 25 2023 *) %o A360911 (PARI) for(n=1, 100, print1(direuler(p=2, n, (1-X+3*X^2)/(1-X)^2)[n], ", ")) %Y A360911 Cf. A048785, A226602, A360909, A360910. %K A360911 nonn,mult %O A360911 1,4 %A A360911 _Vaclav Kotesovec_, Feb 25 2023