Question 111
For integers $a$ and $n \gt 0$, we say that $a$ is *n-expressible* if it can be written as a sum of distinct positive divisors of $n$. The natural number $n$ is *good* if $a$ being *n-expressible* implies $a-1$ being *n-expressible* for all $a \ge 1$.
Determine for which $n$, both $n!$ and $n^n$ are good.
Determine for which $n$, both $n!$ and $n^n$ are good.