Chork's Puzzle 02

Difficulty Rating: 2

In this room, there are 2006 opened lockers, numbered 1-2006. On Day 1, Ella decides to close every second locker. On Day 2, she heads to every third locker and opens it if it is closed and closed it if it is open. On Day 3, Ella repeats her action of day 2 on every fourth locker (ie open it if it is closed and closes it if it is opened.)

She repeats this action on subsequent days, ie. on day n, she heads to every (n+1)th locker and opens it if it is closed and closes it if it is opened. On Day 2005, she heads to the 2006th locker and shuts it and completes her cycle of actions. (At last she can take a break!)

How many lockers are open at the end of day 2005?
If you know the answer, post it in the comments section of this post.