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A035224
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Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s) + Kronecker(m,p)*p^(-2s))^(-1) for m = 42.
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1
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1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 1, 2, 1, 1, 2, 0, 0, 1, 2, 2, 0, 1, 0, 2, 2, 0, 2, 1, 0, 2, 0, 0, 2, 1, 1, 1, 2, 2, 2, 1, 0, 1, 2, 2, 0, 0, 2, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 1, 2, 2, 2, 2, 0, 1
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OFFSET
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1,11
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LINKS
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FORMULA
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a(n) = Sum_{d|n} Kronecker(42, d).
Multiplicative with a(p^e) = 1 if Kronecker(42, p) = 0 (p = 2, 3 or 7), a(p^e) = (1+(-1)^e)/2 if Kronecker(42, p) = -1 (p is in A038922), and a(p^e) = e+1 if Kronecker(42, p) = 1 (p is in A038921 \ {2, 3, 7}).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2*log(2*sqrt(42)+13)/sqrt(42) = 1.005012885517... . (End)
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MATHEMATICA
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a[n_] := DivisorSum[n, KroneckerSymbol[42, #] &]; Array[a, 100] (* Amiram Eldar, Nov 20 2023 *)
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PROG
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(PARI) my(m = 42); direuler(p=2, 101, 1/(1-(kronecker(m, p)*(X-X^2))-X))
(PARI) a(n) = sumdiv(n, d, kronecker(42, d)); \\ Amiram Eldar, Nov 20 2023
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CROSSREFS
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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