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%I #10 Nov 19 2023 01:27:43
%S 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,
%T 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,
%U 0,0,0,3,0,0,2,0,2,4,2,0,5
%N Coefficients in expansion of Dirichlet series Product_p (1-(Kronecker(m,p)+1)*p^(-s)+Kronecker(m,p)*p^(-2s))^(-1) for m = 22.
%H Amiram Eldar, <a href="/A035204/b035204.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(22, d).
%F 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}).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(42*sqrt(22)+197)/sqrt(22) = 1.274160921644... . (End)
%t a[n_] := DivisorSum[n, KroneckerSymbol[22, #] &]; Array[a, 100] (* _Amiram Eldar_, Nov 19 2023 *)
%o (PARI) my(m = 22); direuler(p=2,101,1/(1-(kronecker(m,p)*(X-X^2))-X))
%o (PARI) a(n) = sumdiv(n, d, kronecker(22, d)); \\ _Amiram Eldar_, Nov 19 2023
%Y Cf. A038895, A038896.
%K nonn,easy,mult
%O 1,3
%A _N. J. A. Sloane_
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