155990

First of all I decided that if the top number had to be 15 then I could start at the top and work down to the bottom. First I started with 15 then 8 and 7 and finally the numbers I got were 2,2,2 and 1. I continued doing this and got more and more sets of numbers. eventually I couldn't find any more. This is how I solved this problem.
Numbers I got:
1: 2, 2, 2, 1
2: 4, 2, 1, 2
3: 3, 2, 1, 3
4: 6, 1, 1, 3
5: 2, 3, 1, 1