Number of Prime Divisors ofphik(n), wherephikIs thek-fold Iterate ofphi Original Research Article

In this paper we obtain the distribution of the functionω(phik(n)) which counts the number of distinct prime factors of thek-fold iterate of the Eulerphifunction. With coefficientsak=1/(k+1)! andbk=1/image (k!) we prove thatimage An analogous result is obtained forω(phik(p−1)). This extends the results known through the work of P. Erdös and C. Pomerance, M. R. Murty and V. K. Murty, and I. Kátai.