Central Jr. High has exactly 500 students and 500 lockers. On a certain day the lockers were opened and closed by the students in the following...

Central Jr. High has exactly 500 students and 500 lockers. On a certain day the lockers were opened and closed by the students in the following manner. The first student to enter the locker room opened all the lockers. The second student closed each even numbered locker. The third student changed every third locker, opening each one that was closed and closing each one that was open. The fourth student changed every fourth locker, the fifth student changed every fifth locker, the sixth student changed every sixth locker and so on. After all 500 students had passed through the locker room, opening and closing lockers, how many lockers were open?