Note on the prime divisors of Farey fractions - Kazakevičius, Vytautas; Stakėnas, Vilius (Lietuvos matematikos rinkinys, 2011)
Let P1(n) ≥ P2(n) ≥· · · be the prime divisors of a natural number n arranged in the non-increasing order. The limit distribution of the sequences (log Pi(mn)/ log(mn), i ≥ 1) for m/n ꞓ 2 (lambda1; lambda2), n ≤ x, are considered. It is proved that under some conditions on lambdai the limit distribution of the sequences exists and is closely related to the Poisson–Dirichlet distribution.
Keywords: rational numbers; prime divisors; Poisson-Dirichlet distribution