Question 26
An infinite sequence $ a_1, a_2, \ldots $ consists of positive integers, each of which has at least four positive divisors. 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 N is a divisor of N other than N.
A proper divisor of a positive integer N is a divisor of N other than N.