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A035177
Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -13.
2
1, 0, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 3, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 1
OFFSET
1,7
LINKS
FORMULA
From Amiram Eldar, Nov 17 2023 (Start)
a(n) = Sum_{d|n} Kronecker(-13, d).
Multiplicative with a(13^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-13, p) = -1, and a(p^e) = e+1 if Kronecker(-13, p) = 1 (p is in A296926).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/(3*sqrt(13)) = 0.5808806... . (End)
MATHEMATICA
a[n_] := DivisorSum[n, KroneckerSymbol[-13, #] &]; Array[a, 100] (* Amiram Eldar, Nov 17 2023 *)
PROG
(PARI) my(m = -13); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(-13, d)); \\ Amiram Eldar, Nov 17 2023
CROSSREFS
Cf. A296926.
Sequence in context: A325200 A266909 A276491 * A194591 A070105 A111397
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved