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.
|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.