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.