A035212 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, 2, 1, 1, 1, 0, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 0, 0, 1, 1, 2, 1, 2, 2, 1, 0, 1, 0, 2, 2, 1, 2, 2, 2, 1, 0, 2, 0, 0, 1, 0, 0, 1, 3, 1, 2, 2, 0, 1, 0, 2, 2, 2, 0, 1, 0, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 0, 1, 1
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
a[n_] := DivisorSum[n, KroneckerSymbol[30, #] &]; Array[a, 100] (* Amiram Eldar, Nov 19 2023 *)
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PARI
my(m = 30); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
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PARI
a(n) = sumdiv(n, d, kronecker(30, d)); \\ Amiram Eldar, Nov 19 2023
Formula
From Amiram Eldar, Nov 19 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 A038904), and a(p^e) = e+1 if Kronecker(30, p) = 1 (p is in A097959).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(2*sqrt(30)+11)/sqrt(30) = 1.127932330891... . (End)