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A035208 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 A035208 #9 Nov 19 2023 01:24:48
%S A035208 1,1,0,1,2,0,0,1,1,2,2,0,1,0,0,1,2,1,2,2,0,2,2,0,3,1,0,0,0,0,0,1,0,2,
%T A035208 0,1,2,2,0,2,0,0,0,2,2,2,0,0,1,3,0,1,0,0,4,0,0,0,2,0,0,0,0,1,2,0,2,2,
%U A035208 0,0,0,1,0,2,0,2,0,0,2,2,1
%N A035208 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 A035208 Amiram Eldar, <a href="/A035208/b035208.txt">Table of n, a(n) for n = 1..10000</a>
%F A035208 From _Amiram Eldar_, Nov 19 2023: (Start)
%F A035208 a(n) = Sum_{d|n} Kronecker(26, d).
%F A035208 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 (p is in A038900), and a(p^e) = e+1 if Kronecker(26, p) = 1 (p is in A038899 \ {2, 13}).
%F A035208 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(sqrt(26)+5)/sqrt(26) = 0.907012940471... . (End)
%t A035208 a[n_] := DivisorSum[n, KroneckerSymbol[26, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *)
%o A035208 (PARI) my(m = 26); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o A035208 (PARI) a(n) = sumdiv(n, d, kronecker(26, d)); \\ _Amiram Eldar_, Nov 19 2023
%Y A035208 Cf. A038899, A038900.
%K A035208 nonn,easy,mult
%O A035208 1,5
%A A035208 _N. J. A. Sloane_