On the distribution of the greatest common divisor of the elements in integral part sets

Abstract

It is a classical result that the probability that two positive integers n, m ≤ x are relatively prime tends to 1/ζ(2) = 6/π2 as x → ∞. In this paper, the same result is still true when n and m are restricted to sub-sequences, i.e. Piatetski–Shapiro sequence, Beatty sequence and the floor function set.