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.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A038915, A038916.

Sequence in context: A091395 A248107 A352561 * A227618 A366533 A340683

Adjacent sequences: A035217 A035218 A035219 * A035221 A035222 A035223

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved