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A035220
Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 38.
2
1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 0, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 0, 2, 0, 1
OFFSET
1,11
LINKS
FORMULA
From Amiram Eldar, Nov 20 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 A038916), and a(p^e) = e+1 if Kronecker(38, p) = 1 (p is in A038915 \ {2, 19}).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(6*sqrt(38)+37)/sqrt(38) = 0.698181923868... . (End)
MATHEMATICA
a[n_] := DivisorSum[n, KroneckerSymbol[38, #] &]; Array[a, 100] (* Amiram Eldar, Nov 20 2023 *)
PROG
(PARI) my(m = 38); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(38, d)); \\ Amiram Eldar, Nov 20 2023
CROSSREFS
Sequence in context: A091395 A248107 A352561 * A227618 A366533 A340683
KEYWORD
nonn,easy,mult
STATUS
approved