Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7.
OOOOO |
OOOO O |
OOO OO |
OOO O O |
OO OO O |
OO O O O |
O O O O O |
Find the least value of n for which p(n) is divisible by one million.