A proper divisor of a positive integer N is a positive divisor of N other than N itself.
The infinite sequence a_1, a_2, \cdots consists of positive integers, each of which has at least three proper divisors. For each n\geq 1, the integer a_{n+1} is the sum of the three largest proper divisors of a_n.
Determine all possible values of a_1.
Proposed by Paulius Aleknavičius, Lithuania