OFFSET
1,5
COMMENTS
Coefficients of Dedekind zeta function for the quadratic number field of discriminant 24. See A002324 for formula and Maple code. - N. J. A. Sloane, Mar 22 2022
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
From Amiram Eldar, Oct 17 2022: (Start)
a(n) = Sum_{d|n} Kronecker(6, d).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(5+2*sqrt(6)) / sqrt(6) = 0.935881... . (End)
Multiplicative with a(p^e) = 1 if Kronecker(6, p) = 0 (p = 2 or 3), a(p^e) = (1+(-1)^e)/2 if Kronecker(6, p) = -1 (p is in A038877), and a(p^e) = e+1 if Kronecker(6, p) = 1 (p is in A097934). - Amiram Eldar, Nov 20 2023
MATHEMATICA
a[n_] := If[n < 0, 0, DivisorSum[n, KroneckerSymbol[6, #] &]]; Table[ a[n], {n, 1, 100}] (* G. C. Greubel, Apr 27 2018 *)
PROG
(PARI) my(m=6); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(6, d)); \\ Amiram Eldar, Nov 20 2023
CROSSREFS
Dedekind zeta functions for imaginary quadratic number fields of discriminants -3, -4, -7, -8, -11, -15, -19, -20 are A002324, A002654, A035182, A002325, A035179, A035175, A035171, A035170, respectively.
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved