Rough values of Piatetski-Shapiro sequences

An integer is called y-rough if it is composed solely of primes > y. Let left perpendicular.right perpendicular be the floor function. In this paper, we exhibit an asymptotic formula for the counting function of integers n <= x such that left perpendicular n(c) right perpendicular is y-rough uniformly for a range of y that depends on 1 < c < 2229/1949.