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A035196 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 14.

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%I A035196 #12 Nov 18 2023 06:30:38
%S A035196 1,1,0,1,2,0,1,1,1,2,2,0,2,1,0,1,0,1,0,2,0,2,0,0,3,2,0,1,0,0,2,1,0,0,
%T A035196 2,1,0,0,0,2,0,0,2,2,2,0,2,0,1,3,0,2,0,0,4,1,0,0,0,0,2,2,1,1,4,0,2,0,
%U A035196 0,2,0,1,0,0,0,0,2,0,0,2,1
%N A035196 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 14.
%H A035196 G. C. Greubel, <a href="/A035196/b035196.txt">Table of n, a(n) for n = 1..10000</a>
%F A035196 From _Amiram Eldar_, Nov 18 2023: (Start)
%F A035196 a(n) = Sum_{d|n} Kronecker(14, d).
%F A035196 Multiplicative with a(p^e) = 1 if Kronecker(14, p) = 0 (p = 2 or 7), a(p^e) = (1+(-1)^e)/2 if Kronecker(14, p) = -1 (p is in A038886), and a(p^e) = e+1 if Kronecker(14, p) = 1 (p is in A038885 \ {2, 7}).
%F A035196 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(4*sqrt(14)+15)/(2*sqrt(14)) = 0.908710783123... . (End)
%t A035196 a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[14, #] &]]; Table[ a[n], {n, 1, 100}] (* _G. C. Greubel_, Apr 27 2018 *)
%o A035196 (PARI) my(m=14); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o A035196 (PARI) a(n) = sumdiv(n, d, kronecker(14, d)); \\ _Amiram Eldar_, Nov 18 2023
%Y A035196 Cf. A038885, A038886.
%K A035196 nonn,easy,mult
%O A035196 1,5
%A A035196 _N. J. A. Sloane_