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A035180
Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -10.
2
1, 1, 0, 1, 1, 0, 2, 1, 1, 1, 2, 0, 2, 2, 0, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 2, 0, 2, 0, 0, 0, 1, 0, 0, 2, 1, 2, 2, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 3, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 4, 0, 0, 1, 1
OFFSET
1,7
LINKS
FORMULA
From Amiram Eldar, Nov 17 2023: (Start)
a(n) = Sum_{d|n} Kronecker(-10, d).
Multiplicative with a(p^e) = 1 if Kronecker(-10, p) = 0 (p = 2 or 5), a(p^e) = (1+(-1)^e)/2 if Kronecker(-10, p) = -1 (p is in A296925), and a(p^e) = e+1 if Kronecker(-10, p) = 1.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi/sqrt(10) = 0.993458... . (End)
MATHEMATICA
a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[-10, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)
PROG
(PARI) my(m=-10); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-10, d)); \\ Amiram Eldar, Nov 17 2023
CROSSREFS
Cf. A296925.
Sequence in context: A279126 A210679 A143262 * A163819 A301734 A281185
KEYWORD
nonn,easy,mult
STATUS
approved