There are 1000 lockers in a high school with 1000 students. The
problem begins with the first student opening all 1000 lockers; next
the second student closes lockers 2,4,6,8,10 and so on to locker 1000;
the third student changes the state (opens lockers closed, closes
lockers open) on lockers 3,6,9,12,15 and so on; the fourth student
changes the state of lockers 4,8,12,16 and so on. This goes on until
every student has had a turn.

How many lockers will be open at the end? What is the formula?