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A035204
Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 22.
2
1, 1, 2, 1, 0, 2, 2, 1, 3, 0, 1, 2, 2, 2, 0, 1, 0, 3, 0, 0, 4, 1, 0, 2, 1, 2, 4, 2, 2, 0, 0, 1, 2, 0, 0, 3, 0, 0, 4, 0, 0, 4, 0, 1, 0, 0, 0, 2, 3, 1, 0, 2, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 6, 1, 0, 2, 2, 0, 0, 0, 0, 3, 0, 0, 2, 0, 2, 4, 2, 0, 5
OFFSET
1,3
LINKS
FORMULA
From Amiram Eldar, Nov 19 2023: (Start)
a(n) = Sum_{d|n} Kronecker(22, d).
Multiplicative with a(p^e) = 1 if Kronecker(22, p) = 0 (p = 2 or 11), a(p^e) = (1+(-1)^e)/2 if Kronecker(22, p) = -1 (p is in A038896), and a(p^e) = e+1 if Kronecker(22, p) = 1 (p is in A038895 \ {2, 11}).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(42*sqrt(22)+197)/sqrt(22) = 1.274160921644... . (End)
MATHEMATICA
a[n_] := DivisorSum[n, KroneckerSymbol[22, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)
PROG
(PARI) my(m = 22); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(22, d)); \\ Amiram Eldar, Nov 19 2023
CROSSREFS
Sequence in context: A198727 A294508 A035152 * A349621 A326987 A190775
KEYWORD
nonn,easy,mult
STATUS
approved