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A035196
Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 14.
3
1, 1, 0, 1, 2, 0, 1, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 3, 2, 0, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 3, 0, 2, 0, 0, 4, 1, 0, 0, 0, 0, 2, 2, 1, 1, 4, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1
OFFSET
1,5
LINKS
FORMULA
From Amiram Eldar, Nov 18 2023: (Start)
a(n) = Sum_{d|n} Kronecker(14, d).
Multiplicative with a(p^e) = 1 if Kronecker(14, p) = 0 (p = 2 or 7), a(p^e) = (1+(-1)^e)/2 if Kronecker(14, p) = -1 (p is in A038886), and a(p^e) = e+1 if Kronecker(14, p) = 1 (p is in A038885 \ {2, 7}).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(4*sqrt(14)+15)/(2*sqrt(14)) = 0.908710783123... . (End)
MATHEMATICA
a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[14, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)
PROG
(PARI) my(m=14); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(14, d)); \\ Amiram Eldar, Nov 18 2023
CROSSREFS
Sequence in context: A029402 A330443 A268479 * A287475 A158020 A051160
KEYWORD
nonn,easy,mult
STATUS
approved