Coin Partitions

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 \( p(5) = 7\).

\[ \begin{align} &OOOOO\\ &OOOO\ \ O\\ &OOO\ \ OO\\ &OOO\ \ O\ \ O\\ &OO\ \ OO\ \ O\\ &OO\ \ O\ \ O\ \ O\\ &O\ \ O\ \ O\ \ O\ \ O \end{align} \]

Find the least value of n for which \( p(n) \) is divisible by one million.