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 A327341 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. 2
 1, 1, 9, 8, 5, 9, 49, 16, 81, 50, 121, 72, 169, 49, 5, 64, 289, 54, 361, 200, 441, 242, 529, 288, 625, 338, 729, 392, 841, 225, 31, 128, 363, 578, 1225, 216, 1369, 361, 1521, 40, 1681, 882, 1849, 968, 75, 1058, 2209, 128, 2401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The corresponding numerators are given in A327340. For details see A327340, also for the Dedekind's psi function, the rationals and the limit. REFERENCES Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, p. 100, Satz 2. LINKS Table of n, a(n) for n=1..49. FORMULA 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. EXAMPLE See A327340. MATHEMATICA 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 *) PROG (PARI) dpsi(n) = n * sumdivmult(n, d, issquarefree(d)/d); \\ A001615 a(n) = denominator(sum(k=1, n, dpsi(k))/n^2); \\ Michel Marcus, Sep 18 2023 CROSSREFS Cf. A327340. Sequence in context: A094141 A200292 A155791 * A059068 A059069 A084660 Adjacent sequences: A327338 A327339 A327340 * A327342 A327343 A327344 KEYWORD nonn,frac,easy AUTHOR Wolfdieter Lang, Sep 03 2019 STATUS approved

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Last modified June 13 10:09 EDT 2024. Contains 373383 sequences. (Running on oeis4.)