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Coin partitions

Problem 78

Published on Friday, 10th September 2004, 06:00 pm; Solved by 10224; Difficulty rating: 30%

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.