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A327341
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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.
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2
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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
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OFFSET
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1,3
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COMMENTS
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The corresponding numerators are given in A327340.
For details see A327340, also for the Dedekind's psi function, the rationals and the limit.
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REFERENCES
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Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, p. 100, Satz 2.
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LINKS
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Table of n, a(n) for n=1..49.
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FORMULA
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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.
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EXAMPLE
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See A327340.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A327340.
Sequence in context: A094141 A200292 A155791 * A059068 A059069 A084660
Adjacent sequences: A327338 A327339 A327340 * A327342 A327343 A327344
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang, Sep 03 2019
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STATUS
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approved
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