Coin Partitions
Problem 78
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
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.