MathDB

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.

5