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 A035217 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 35. 2

%I #9 Nov 19 2023 01:26:37

%S 1,0,0,1,1,0,1,0,1,0,0,0,2,0,0,1,2,0,2,1,0,0,2,0,1,0,0,1,2,0,2,0,0,0,

%T 1,1,0,0,0,0,0,0,2,0,1,0,0,0,1,0,0,2,0,0,0,0,0,0,2,0,0,0,1,1,2,0,2,2,

%U 0,0,0,0,2,0,0,2,0,0,0,1,1

%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 35.

%H Amiram Eldar, <a href="/A035217/b035217.txt">Table of n, a(n) for n = 1..10000</a>

%F From _Amiram Eldar_, Nov 19 2023: (Start)

%F a(n) = Sum_{d|n} Kronecker(35, d).

%F Multiplicative with a(p^e) = 1 if Kronecker(35, p) = 0 (p = 5 or 7), a(p^e) = (1+(-1)^e)/2 if Kronecker(35, p) = -1 (p is in A038912), and a(p^e) = e+1 if Kronecker(35, p) = 1 (p is in A038911 \ {5, 7}).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4*log(sqrt(35)+6)/(3*sqrt(35)) = 0.558452854172... . (End)

%t a[n_] := DivisorSum[n, KroneckerSymbol[35, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *)

%o (PARI) my(m = 35); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

%o (PARI) a(n) = sumdiv(n, d, kronecker(35, d)); \\ _Amiram Eldar_, Nov 19 2023

%Y Cf. A038911, A038912.

%K nonn,easy,mult

%O 1,13

%A _N. J. A. Sloane_

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Last modified September 13 07:32 EDT 2024. Contains 375870 sequences. (Running on oeis4.)