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A035226 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 44. 1

%I #10 Nov 20 2023 11:40:46

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

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

%U 0,4,0,1,0,2,0,2,2,0,2,2,1

%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 44.

%H Amiram Eldar, <a href="/A035226/b035226.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(44, d).

%F Multiplicative with a(p^e) = 1 if Kronecker(44, p) = 0 (p = 2 or 11), a(p^e) = (1+(-1)^e)/2 if Kronecker(44, p) = -1 (p is in A296936), and a(p^e) = e+1 if Kronecker(44, p) = 1 (p is in A296935).

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(3*sqrt(11)+10)/sqrt(44) = 0.902490644956... . (End)

%t a[n_] := DivisorSum[n, KroneckerSymbol[44, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 20 2023 *)

%o (PARI) my(m = 44); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))

%o (PARI) a(n) = sumdiv(n, d, kronecker(44, d)); \\ _Amiram Eldar_, Nov 20 2023

%Y Cf. A296935, A296936.

%K nonn,easy,mult

%O 1,5

%A _N. J. A. Sloane_

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)