Question 109
Assume that $n$ is a composite positive integer. For each its proper divisor $d$, we write down the number $d+1$ on the board. Find all values of $n$ for which the written numbers appear to be exactly all the proper divisors of some positive integer $m$. (A proper divisor of a positive integer $a \gt 1$ is any its positive divisor distinct from 1 and $a$.)