## Compositions with the Euler and Carmichael Functions

Banks, William David, 1964-

Luca, Florian

Saidak, Filip

Stănică, Pantelimon

##### 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

Mathematics publications (MU)

##### Citation

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