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A358780 Dirichlet g.f.: zeta(s) * zeta(2*s) * zeta(3*s) * zeta(4*s).

%I A358780 #28 Mar 14 2023 13:02:45
%S A358780 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,5,1,2,1,2,1,1,1,3,2,1,3,2,1,1,1,6,1,1,
%T A358780 1,4,1,1,1,3,1,1,1,2,2,1,1,5,2,2,1,2,1,3,1,3,1,1,1,2,1,1,2,9,1,1,1,2,
%U A358780 1,1,1,6,1,1,2,2,1,1,1,5,5,1,1,2,1,1,1,3
%N A358780 Dirichlet g.f.: zeta(s) * zeta(2*s) * zeta(3*s) * zeta(4*s).
%C A358780 a(n) = A000688(n) for n < 32.
%H A358780 Vaclav Kotesovec, <a href="/A358780/b358780.txt">Table of n, a(n) for n = 1..10000</a>
%F A358780 Multiplicative with a(p^e) = A001400(e).
%F A358780 Sum_{k=1..n} a(k) ~ Pi^6*zeta(3)*n/540 + Pi^2*zeta(1/2)*zeta(3/2)*sqrt(n)/6 + zeta(1/3)*zeta(2/3)*zeta(4/3)*n^(1/3) + zeta(1/4)*zeta(1/2)*zeta(3/4)*n^(1/4).
%o A358780 (PARI) for(n=1, 200, print1(direuler(p=2, n, 1/(1 - X)/(1 - X^2)/(1 - X^3)/(1 - X^4))[n], ", "))
%Y A358780 Cf. A046951, A322885, A000688.
%Y A358780 Cf. A001400, A063966.
%K A358780 nonn,mult
%O A358780 1,4
%A A358780 _Vaclav Kotesovec_, Mar 14 2023