1000 Locker Problem

I think that whatever number or person, who changed the locker multiplied by itself, are the ones who are open (showed in diagram above)
1x1, 2x2, 3x3 etc… so each locker gets it’s state changed as many times as its divisors. So the numbers with an odd number of divisors are left open. Like 16, its divisors are 1, 2, and 4,8,16. The numbers with an even number of divisors are closed. Like 20, its divisors are 1, 2,4,5,10,20. So you are left with 31 lockers open. So locker 1, 4,9,16,25,36,49 etc… You keep on going until you get 1000. That’s how you solve the 1000 locker problem.