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.