Question 92
For $n = \prod_i p_i^{e_i}$ ($p_i$ primes, $e_i$ positive integers), define $\psi(n) = \prod_i (p_i + 1)^{e_i - 1}$. Show that by repeated application of $\psi$, we may transform any starting number into a number of the form $2^m$ for $m \ge 0$.