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A035167
Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -23.
2
1, 2, 2, 3, 0, 4, 0, 4, 3, 0, 0, 6, 2, 0, 0, 5, 0, 6, 0, 0, 0, 0, 1, 8, 1, 4, 4, 0, 2, 0, 2, 6, 0, 0, 0, 9, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 10, 1, 2, 0, 6, 0, 8, 0, 0, 0, 4, 2, 0, 0, 4, 0, 7, 0, 0, 0, 0, 2, 0, 2, 12, 2, 0, 2, 0, 0, 8, 0, 0, 5
OFFSET
1,2
FORMULA
From Amiram Eldar, Nov 17 2023: (Start)
a(n) = Sum_{d|n} Kronecker(-23, d).
Multiplicative with a(23^e) = 1, a(p^e) = (1+(-1)^e)/2 if Kronecker(-23, p) = -1 (p is in A191065), and a(p^e) = e+1 if Kronecker(-23, p) = 1 (p is in A191021).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3*Pi/sqrt(23) = 1.965202... . (End)
MATHEMATICA
a[ n_] := If[ n < 1, 0, Sum[ KroneckerSymbol[ -23, d], { d, Divisors[ n]}]]; (* Michael Somos, Jan 24 2021 *)
PROG
(PARI) my(m = -23); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) {a(n) = if( n<1, 0, sumdiv(n, d, kronecker( -23, d)))}; /* Michael Somos, Jan 24 2021 */
CROSSREFS
Sequence in context: A213081 A127446 A046157 * A071448 A071449 A035189
KEYWORD
nonn,easy,mult
AUTHOR
STATUS
approved