A035212 Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 30.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 0, 0, 1, 1, 2, 1, 2, 2, 1, 0, 1, 0, 2, 2, 1, 2, 2, 2, 1, 0, 2, 0, 0, 1, 0, 0, 1, 3, 1, 2, 2, 0, 1, 0, 2, 2, 2, 0, 1, 0, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 0, 1, 1

Offset

1,7

Links

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

Formula

From Amiram Eldar, Nov 19 2023: (Start)

a(n) = Sum_{d|n} Kronecker(30, d).

Multiplicative with a(p^e) = 1 if Kronecker(30, p) = 0 (p = 2, 3 or 5), a(p^e) = (1+(-1)^e)/2 if Kronecker(30, p) = -1 (p is in A038904), and a(p^e) = e+1 if Kronecker(30, p) = 1 (p is in A097959).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(2*sqrt(30)+11)/sqrt(30) = 1.127932330891... . (End)

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[30, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)

Prog

(PARI) my(m = 30); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(30, d)); \\ Amiram Eldar, Nov 19 2023

Crossrefs

Cf. A038904, A097959.

Sequence in context: A227752 A316771 A306269 * A318133 A068029 A158208

Adjacent sequences: A035209 A035210 A035211 * A035213 A035214 A035215

Keyword

nonn,easy,mult

Author

N. J. A. Sloane

Status

approved