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