PL-OM 1996 Problem 5

Let $p(k)$ be the smallest prime not dividing $k$ . Put $q(k) = 1$ if $p(k) = 2$ , or the product of all primes $< p(k)$ if $p(k) > 2$ . Define the sequence $x_0, x_1, x_2, ...$ by $x_0 = 1$ , $x_{n+1} = \frac{x_np(x_n)}{q(x_n)}$ . Find all $n$ such that $x_n = 111111$