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%I #10 Nov 20 2023 10:49:08
%S 1,0,2,1,0,0,2,0,3,0,0,2,2,0,0,1,2,0,2,0,4,0,0,0,1,0,4,2,0,0,0,0,0,0,
%T 0,3,0,0,4,0,2,0,1,0,0,0,0,2,3,0,4,2,2,0,0,0,4,0,0,0,0,0,6,1,0,0,0,2,
%U 0,0,2,0,0,0,2,2,0,0,0,0,5
%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 43.
%H Amiram Eldar, <a href="/A035225/b035225.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Amiram Eldar_, Nov 20 2023: (Start)
%F a(n) = Sum_{d|n} Kronecker(43, d).
%F Multiplicative with a(43^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(43, p) = -1 (p is in A038924), and a(p^e) = e+1 if Kronecker(43, p) = 1 (p is in A038923 \ {43}).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(531*sqrt(43)+3482)/(3*sqrt(43)) = 0.899590009877... . (End)
%t a[n_] := DivisorSum[n, KroneckerSymbol[43, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 20 2023 *)
%o (PARI) my(m = 43); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o (PARI) a(n) = sumdiv(n, d, kronecker(43, d)); \\ _Amiram Eldar_, Nov 20 2023
%Y Cf. A038923, A038924.
%K nonn,easy,mult
%O 1,3
%A _N. J. A. Sloane_
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