A035228 - OEIS

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A035228

Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 46.

1, 1, 2, 1, 2, 2, 2, 1, 3, 2, 0, 2, 0, 2, 4, 1, 0, 3, 0, 2, 4, 0, 1, 2, 3, 0, 4, 2, 0, 4, 0, 1, 0, 0, 4, 3, 2, 0, 0, 2, 2, 4, 0, 0, 6, 1, 0, 2, 3, 3, 0, 0, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 6, 1, 0, 0, 0, 0, 2, 4, 0, 3, 2, 2, 6, 0, 0, 0, 2, 2, 5

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OFFSET

1,3

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(46, d).

Multiplicative with a(p^e) = 1 if Kronecker(46, p) = 0 (p = 2 or 23), a(p^e) = (1+(-1)^e)/2 if Kronecker(46, p) = -1 (p is in A038926), and a(p^e) = e+1 if Kronecker(46, p) = 1 (p is in A038925 \ {2, 23}).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(3588*sqrt(46)+24335)/sqrt(46) = 1.591314213442... . (End)

MATHEMATICA

a[n_] := DivisorSum[n, KroneckerSymbol[46, #] &]; Array[a, 100] (* Amiram Eldar, Nov 20 2023 *)

PROG

(PARI) my(m = 46); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))

(PARI) a(n) = sumdiv(n, d, kronecker(46, d)); \\ Amiram Eldar, Nov 20 2023

CROSSREFS

Cf. A038925, A038926.

Sequence in context: A211270 A071414 A067148 * A035164 A023588 A175242

Adjacent sequences: A035225 A035226 A035227 * A035229 A035230 A035231

KEYWORD

nonn,easy,mult

AUTHOR

N. J. A. Sloane

STATUS

approved