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Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -26.
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%I #11 Nov 17 2023 11:20:05

%S 1,1,2,1,2,2,2,1,3,2,0,2,1,2,4,1,2,3,0,2,4,0,0,2,3,1,4,2,0,4,2,1,0,2,

%T 4,3,2,0,2,2,0,4,2,0,6,0,2,2,3,3,4,1,0,4,0,2,0,0,0,4,0,2,6,1,2,0,0,2,

%U 0,4,2,3,0,2,6,0,0,2,0,2,5

%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -26.

%H Amiram Eldar, <a href="/A035164/b035164.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Amiram Eldar_, Nov 17 2023: (Start)

%F a(n) = Sum_{d|n} Kronecker(-26, d).

%F Multiplicative with a(p^e) = 1 if Kronecker(-26, p) = 0 (p = 2 or 13), a(p^e) = (1+(-1)^e)/2 if Kronecker(-26, p) = -1, and a(p^e) = e+1 if Kronecker(-26, p) = 1.

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*Pi/sqrt(26) = 1.84835102... . (End)

%t a[n_] := DivisorSum[n, KroneckerSymbol[-26, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 17 2023 *)

%o (PARI) my(m = -26); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

%o (PARI) a(n) = sumdiv(n, d, kronecker(-26, d)); \\ _Amiram Eldar_, Nov 17 2023

%K nonn,easy,mult

%O 1,3

%A _N. J. A. Sloane_