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A035211 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 29.

%I A035211 #12 Nov 19 2023 01:26:20
%S A035211 1,0,0,1,2,0,2,0,1,0,0,0,2,0,0,1,0,0,0,2,0,0,2,0,3,0,0,2,1,0,0,0,0,0,
%T A035211 4,1,0,0,0,0,0,0,0,0,2,0,0,0,3,0,0,2,2,0,0,0,0,0,2,0,0,0,2,1,4,0,2,0,
%U A035211 0,0,2,0,0,0,0,0,0,0,0,2,1
%N A035211 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 29.
%C A035211 Coefficients of Dedekind zeta function for the quadratic number field of discriminant 29. See A002324 for formula and Maple code. - _N. J. A. Sloane_, Mar 22 2022
%H A035211 Amiram Eldar, <a href="/A035211/b035211.txt">Table of n, a(n) for n = 1..10000</a>
%F A035211 From _Amiram Eldar_, Nov 19 2023: (Start)
%F A035211 a(n) = Sum_{d|n} Kronecker(29, d).
%F A035211 Multiplicative with a(29^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(29, p) = -1 (p is in A038902), and a(p^e) = e+1 if Kronecker(29, p) = 1 (p is in A191022).
%F A035211 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log((sqrt(29)+5)/2)/sqrt(29) = 0.611766289562... . (End)
%t A035211 a[n_] := DivisorSum[n, KroneckerSymbol[29, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *)
%o A035211 (PARI) my(m = 29); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o A035211 (PARI) a(n) = sumdiv(n, d, kronecker(29, d)); \\ _Amiram Eldar_, Nov 19 2023
%Y A035211 Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
%Y A035211 Dedekind zeta functions for real quadratic number fields of discriminants 5, 8, 12, 13, 17, 21, 24, 28, 29, 33, 37, 40 are A035187, A035185, A035194, A035195, A035199, A035203, A035188, A035210, A035211, A035215, A035219, A035192, respectively.
%Y A035211 Cf. A038902, A191022.
%K A035211 nonn,easy,mult
%O A035211 1,5
%A A035211 _N. J. A. Sloane_