Hypercyclic and chaotic convolution operators associated with the Dunkl operator on <Emphasis Type=?Bold?>C</Emphasis>

Abstract

We show that there exist infinitely many positive integers m not of the form n -o( n ) for any positive integer n . Here, o( n ) stands for the number of distinct prime factors of n . A similar result holds with o( n ) replaced by the total number of prime factors of n (counting multiplicities), or by the number of divisors of n .