A035160 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, 0, 1, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 0, 1, 0, 2, 2, 1, 1, 2, 1, 0, 2, 1, 2, 1, 2, 2, 0, 1, 2, 0, 2, 1, 0, 0, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 0, 1, 2, 0, 0, 2, 2, 1, 0, 2, 0, 1, 2, 2, 2, 2, 2, 0, 0, 1, 0, 2, 1, 0, 0, 2, 2, 1, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A191023, A191066.

Programs

Mathematica

a[n_] := DivisorSum[n, KroneckerSymbol[-30, #] &]; Array[a, 100] (* Amiram Eldar, Nov 17 2023 *)

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 17 2023

Formula

From Amiram Eldar, Nov 17 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 A191066), and a(p^e) = e+1 if Kronecker(-30, p) = 1 (p is in A191023).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/sqrt(30) = 1.1471474... . (End)