On sparsely totient numbers

Abstract

Let (n) denote Euler's totient function, defined forn> 1 by p\n Let F be the set of integers n > 1 with the property that (m) > (n) whenever m > . The purpose of this paper is to establish a number of results about the set F. For example, we shall prove that each prime divides all sufficiently large elements of F, each positive integer divides some element of F, and that the ratio of successive elements of F approaches 1.