## Compositions with the Euler and Carmichael Functions

##### Abstract

Let ' and _ 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 '(_(n)) = _('(n)). We also study the normal order of the function '(_(n))/_('(n)).

##### Part of

##### Citation

Abh. Math. Sem. Hamburg, 75 (2005), 215-243.