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%I #14 Sep 04 2019 21:17:24
%S 1,1,9,8,5,9,49,16,81,50,121,72,169,49,5,64,289,54,361,200,441,242,
%T 529,288,625,338,729,392,841,225,31,128,363,578,1225,216,1369,361,
%U 1521,40,1681,882,1849,968,75,1058,2209,128,2401
%N Denominators of the rationals r(n) = (1/n^2)*Phi_1(n), with Phi_1(n) = Sum{k=1..n} psi(k), with Dedekind's psi function.
%C The corresponding numerators are given in A327340.
%C For details see A327340, also for the Dedekind's psi function, the rationals and the limit.
%D Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, p. 100, Satz 2.
%F a(n) = denominator(r(n)), with the rationals r(n) = (1/n^2)*Sum{k=1..n}(k*Product_{p|k}(1 + 1/p)), with distinct prime p divisors of k (with the empty product set to 1 for k = 1), for n >= 1.
%e See A327340.
%t psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); a[n_] := Denominator[Sum[psi[k], {k, 1, n}]/n^2]; Array[a, 50] (* _Amiram Eldar_, Sep 03 2019 *)
%Y Cf. A327340.
%K nonn,frac,easy
%O 1,3
%A _Wolfdieter Lang_, Sep 03 2019
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