## Compositions with the Euler and Carmichael Functions

by
W. D. Banks
,
F. Luca
,
F. Saidak
,
P. Stănică

### BibTeX

@MISC{Banks_compositionswith,

author = {W. D. Banks and F. Luca and F. Saidak and P. Stănică},

title = {Compositions with the Euler and Carmichael Functions},

year = {}

}

### OpenURL

### Abstract

Abstract. Let ϕ and λ be the Euler and Carmichael functions, respectively. In this paper, we establish lower and upper bounds for the number of positive integers n ≤ x such that ϕ(λ(n)) = λ(ϕ(n)). We also study the normal order of the function ϕ(λ(n))/λ(ϕ(n)). 1