  Let $\omega^*(n)$ denote the number of divisors of $n$ that are shifted
primes, that is, the number of divisors of $n$ of the form $p-1$, with $p$
prime. Studied by Prachar in an influential paper from 70 years ago, the higher
moments of $\omega^*(n)$ are still somewhat a mystery. This paper addresses
these higher moments and considers other related problems.
