A035165 - OEIS

A035165

Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = -25.

1, 2, 0, 3, 1, 0, 0, 4, 1, 2, 0, 0, 2, 0, 0, 5, 2, 2, 0, 3, 0, 0, 0, 0, 1, 4, 0, 0, 2, 0, 0, 6, 0, 4, 0, 3, 2, 0, 0, 4, 2, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 6, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 7, 2, 0, 0, 6, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 5, 1

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OFFSET

1,2

LINKS

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

FORMULA

From Amiram Eldar, Nov 17 2023: (Start)

a(n) = Sum_{d|n} Kronecker(-25, d).

Multiplicative with a(5^e) = 1, a(p^e) = (1+(-1)^e)/2 if p == 3 (mod 4) (p is in A002145), and a(p^e) = e+1 if p = 2 or p > 5 and p == 1 (mod 4) (p = 2 or p is in A002144 \ {5}).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*Pi/5 = 1.256637... (A019694). (End)

MATHEMATICA

a[n_] := DivisorSum[n, KroneckerSymbol[-25, #] &]; Array[a, 100] (* Amiram Eldar, Nov 17 2023 *)

PROG

(PARI) my(m = -25); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))

(PARI) a(n) = sumdiv(n, d, kronecker(-25, d)); \\ Amiram Eldar, Nov 17 2023

CROSSREFS

Cf. A002144, A002145, A019694.

Sequence in context: A240606 A335889 A324379 * A290256 A303110 A079133

Adjacent sequences: A035162 A035163 A035164 * A035166 A035167 A035168

KEYWORD

nonn,easy,mult

AUTHOR

N. J. A. Sloane.

STATUS

approved