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%I #8 Sep 15 2023 05:52:45
%S 1,2,2,3,2,4,2,0,3,4,2,6,2,4,4,-3,2,6,2,6,4,4,2,0,3,4,-5,6,2,8,2,-6,4,
%T 4,4,9,2,4,4,0,2,8,2,6,6,4,2,-6,3,6,4,6,2,-10,4,0,4,4,2,12,2,4,6,-9,4,
%U 8,2,6,4,8,2,0,2,4,6,6,4,8,2,-6,-13,4,2,12
%N Dirichlet g.f.: zeta(s)^2/zeta(3*s-2).
%H Vaclav Kotesovec, <a href="/A359302/b359302.txt">Table of n, a(n) for n = 1..10000</a>
%F Sum_{k=1..n} a(k) ~ 3*n.
%F Multiplicative with a(p) = 2, and a(p^e) = 3 - (e-2)*(p^2-1) for e >= 2. - _Amiram Eldar_, Sep 15 2023
%t f[p_, e_] := 3 - (e-2)*(p^2-1); f[p_, 1] = 2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Sep 15 2023 *)
%o (PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - p^2*X^3)/(1-X)^2)[n], ", "))
%Y Cf. A344326.
%K sign,easy,mult
%O 1,2
%A _Vaclav Kotesovec_, Dec 25 2022