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%I #10 Nov 19 2023 01:26:47
%S 1,1,1,1,0,1,2,1,1,0,0,1,0,2,0,1,2,1,0,0,2,0,2,1,1,0,1,2,0,0,2,1,0,2,
%T 0,1,0,0,0,0,2,2,0,0,0,2,2,1,3,1,2,0,0,1,0,2,0,0,0,0,0,2,2,1,0,0,0,2,
%U 2,0,2,1,2,0,1,0,0,0,2,0,1
%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 18.
%H Amiram Eldar, <a href="/A035200/b035200.txt">Table of n, a(n) for n = 1..10000</a>
%F From _Amiram Eldar_, Nov 19 2023: (Start)
%F a(n) = Sum_{d|n} Kronecker(18, d).
%F Multiplicative with a(p^e) = 1 if Kronecker(18, p) = 0 (p = 2 or 3), a(p^e) = (1+(-1)^e)/2 if Kronecker(18, p) = -1 (p is in A003629 \ {3}), and a(p^e) = e+1 if Kronecker(18, p) = 1 (p is in A001132).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4*log(sqrt(2)+1)/(3*sqrt(2)) = 0.830966986853... . (End)
%t a[n_] := DivisorSum[n, KroneckerSymbol[18, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *)
%o (PARI) my(m = 18); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o (PARI) a(n) = sumdiv(n, d, kronecker(18, d)); \\ _Amiram Eldar_, Nov 19 2023
%Y Cf. A001132, A003629.
%K nonn,easy,mult
%O 1,7
%A _N. J. A. Sloane_
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