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A035216 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 34.

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%I A035216 #9 Nov 19 2023 01:25:02
%S A035216 1,1,2,1,2,2,0,1,3,2,2,2,0,0,4,1,1,3,0,2,0,2,0,2,3,0,4,0,2,4,0,1,4,1,
%T A035216 0,3,2,0,0,2,0,0,0,2,6,0,2,2,1,3,2,0,0,4,4,0,0,2,0,4,2,0,0,1,0,4,0,1,
%U A035216 0,0,0,3,0,2,6,0,0,0,0,2,5
%N A035216 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 34.
%H A035216 Amiram Eldar, <a href="/A035216/b035216.txt">Table of n, a(n) for n = 1..10000</a>
%F A035216 From _Amiram Eldar_, Nov 19 2023: (Start)
%F A035216 a(n) = Sum_{d|n} Kronecker(34, d).
%F A035216 Multiplicative with a(p^e) = 1 if Kronecker(34, p) = 0 (p = 2 or 17), a(p^e) = (1+(-1)^e)/2 if Kronecker(34, p) = -1 (p is in A038910), and a(p^e) = e+1 if Kronecker(34, p) = 1 (p is in A191025).
%F A035216 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(6*sqrt(34)+35)/sqrt(34) = 1.457151825131... . (End)
%t A035216 a[n_] := DivisorSum[n, KroneckerSymbol[34, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *)
%o A035216 (PARI) my(m = 34); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o A035216 (PARI) a(n) = sumdiv(n, d, kronecker(34, d)); \\ _Amiram Eldar_, Nov 19 2023
%Y A035216 Cf. A038910, A191025.
%K A035216 nonn,easy,mult
%O A035216 1,3
%A A035216 _N. J. A. Sloane_