1. Introduction. If m and n are two integers chosen at random, the probability that they are relatively prime (2, p. 267) is 6π-2. This result may still hold when m and n are functionally related. Thus, Watson (3) recently proved that for α irrational, the positive integers n for which (n, [αn]) = 1, have density 6π-2. A different proof of a slightly more general result was given by Estermann (1).