Smooth Values of the Iterates of the Euler Phi-Function

Abstract

AbstractLet ϕ(n) be the Euler phi-function, define ϕ0(n) = n and ϕk+1(n) = ϕ(ϕk(n)) for all k ≥ 0. We will determine an asymptotic formula for the set of integers n less than x for which ϕk(n) is y-smooth, conditionally on a weak form of the Elliott–Halberstam conjecture.