Question 4
An infinite sequence $a_1$, $a_2$, … consists of positive integers each of which has at least three proper divisors. Suppose that for each $n\geq 1$, $a_{n+1}$ is the sum of the three largest proper divisors of $a_n$. Determine all possible values of $a_1$. A proper divisor of a positive integer is a positive divisor other than the integer itself.