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A035152 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -38.

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%I A035152 #11 Nov 17 2023 11:21:46
%S A035152 1,1,2,1,0,2,2,1,3,0,0,2,2,2,0,1,2,3,1,0,4,0,2,2,1,2,4,2,2,0,0,1,0,2,
%T A035152 0,3,2,1,4,0,0,4,0,0,0,2,2,2,3,1,4,2,2,4,0,2,2,2,2,0,0,0,6,1,0,0,2,2,
%U A035152 4,0,0,3,2,2,2,1,0,4,0,0,5
%N A035152 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -38.
%H A035152 G. C. Greubel, <a href="/A035152/b035152.txt">Table of n, a(n) for n = 1..10000</a>
%F A035152 From _Amiram Eldar_, Nov 17 2023: (Start)
%F A035152 a(n) = Sum_{d|n} Kronecker(-38, d).
%F A035152 Multiplicative with a(p^e) = 1 if Kronecker(-38, p) = 0 (p = 2 or 19), a(p^e) = (1+(-1)^e)/2 if Kronecker(-38, p) = -1 (p is in A191069), and a(p^e) = e+1 if Kronecker(-38, p) = 1 (p is in A191028).
%F A035152 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*Pi/sqrt(38) = 1.5289008... . (End)
%t A035152 a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-38, #] &]];
%t A035152 Table[a[n], {n, 1, 100}] (* _G. C. Greubel_, Apr 25 2018 *)
%o A035152 (PARI) my(m=-38); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o A035152 (PARI) a(n) = sumdiv(n, d, kronecker(-38, d)); \\ _Amiram Eldar_, Nov 17 2023
%Y A035152 Cf. A191028, A191069.
%K A035152 nonn,easy,mult
%O A035152 1,3
%A A035152 _N. J. A. Sloane_