  We study the distribution of large prime factors of a random element $u$ of
arithmetic sequences satisfying simple regularity and equidistribution
properties. We show that if such an arithmetic sequence has level of
distribution $1$ the large prime factors of $u$ tend to a Poisson-Dirichlet
process, while if the sequence has any positive level of distribution the
correlation functions of large prime factors tend to a Poisson-Dirichlet
process against test functions of restricted support. For sequences with
positive level of distribution, we also estimate the probability the largest
prime factor of $u$ is greater than $u^{1-\epsilon}$, showing that this
probability is $O(\epsilon)$.
  Examples of sequences described include shifted primes and values of
single-variable irreducible polynomials.
  The proofs involve (i) a characterization of the Poisson-Dirichlet process
due to Arratia-Kochman-Miller and (ii) an upper bound sieve.
