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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
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
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.)