

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
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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_{pk}(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 *)


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



