A035152 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -38.
1, 1, 2, 1, 0, 2, 2, 1, 3, 0, 0, 2, 2, 2, 0, 1, 2, 3, 1, 0, 4, 0, 2, 2, 1, 2, 4, 2, 2, 0, 0, 1, 0, 2, 0, 3, 2, 1, 4, 0, 0, 4, 0, 0, 0, 2, 2, 2, 3, 1, 4, 2, 2, 4, 0, 2, 2, 2, 2, 0, 0, 0, 6, 1, 0, 0, 2, 2, 4, 0, 0, 3, 2, 2, 2, 1, 0, 4, 0, 0, 5
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-38, #] &]]; Table[a[n], {n, 1, 100}] (* G. C. Greubel, Apr 25 2018 *) -
PARI
my(m=-38); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
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PARI
a(n) = sumdiv(n, d, kronecker(-38, d)); \\ Amiram Eldar, Nov 17 2023
Formula
From Amiram Eldar, Nov 17 2023: (Start)
a(n) = Sum_{d|n} Kronecker(-38, d).
Multiplicative with a(p^e) = 1 if Kronecker(-38, p) = 0 (p = 2 or 19), a(p^e) = (1+(-1)^e)/2 if Kronecker(-38, p) = -1 (p is in A191069), and a(p^e) = e+1 if Kronecker(-38, p) = 1 (p is in A191028).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*Pi/sqrt(38) = 1.5289008... . (End)