The 100 Lockers

The problem

A hallway has 100 lockers, all closed. 100 students walk past them, one at a time:

Student 1 toggles every locker (opens all 100).
Student 2 toggles every 2nd locker.
Student 3 toggles every 3rd locker.
...
Student $k$ toggles every $k$ th locker.
...
Student 100 toggles only locker 100.

After all 100 students walk by, which lockers are open?