CONO-SUR 2020 Problem 5

There is a pile with $15$ coins on a table. At each step, Pedro choses one of the piles in the table with $a>1$ coins and divides it in two piles with $b\geq1$ and $c\geq1$ coins and writes in the board the product $abc$ . He continues until there are $15$ piles with $1$ coin each. Determine all possible values that the final sum of the numbers in the board can have.