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%I #11 Nov 18 2023 06:30:15
%S 1,0,1,1,1,0,2,0,1,0,0,1,0,0,1,1,0,0,0,1,2,0,2,0,1,0,1,2,2,0,0,0,0,0,
%T 2,1,0,0,0,0,2,0,2,0,1,0,2,1,3,0,0,0,0,0,0,0,0,0,0,1,2,0,2,1,0,0,2,0,
%U 2,0,0,0,0,0,1,0,0,0,0,1,1
%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -45.
%H G. C. Greubel, <a href="/A035145/b035145.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Amiram Eldar_, Nov 18 2023: (Start)
%F a(n) = Sum_{d|n} Kronecker(-45, d).
%F Multiplicative with a(p^e) = 1 if Kronecker(-45, p) = 0 (p = 3 or 5), a(p^e) = (1+(-1)^e)/2 if Kronecker(-45, p) = -1, and a(p^e) = e+1 if Kronecker(-45, p) = 1.
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4*Pi/(9*sqrt(5)) = 0.624427... . (End)
%t a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-45, #] &]];
%t Table[a[n], {n, 1, 100}] (* _G. C. Greubel_, Apr 25 2018 *)
%o (PARI) my(m=-45); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o (PARI) a(n) = sumdiv(n, d, kronecker(-45, d)); \\ _Amiram Eldar_, Nov 18 2023
%K nonn,easy,mult
%O 1,7
%A _N. J. A. Sloane_
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