Re: [math-fun] Locker puzzle

Which lockers are open at noon?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The lockers that are open should be the ones where the number of divisors of their locker number less one (because we don't switch for divisibility by 1) is odd. Equivalently, the lockers that are closed are the ones where the number of divisors of their locker number is odd. DivisorSigma[0,Range[25]] {1,2,2,3,2,4,2,4,3,4,2,6,2,4,4,5,2,6,2,6,4,4,2,8,3} Seemingly, an odd number of divisors happens for squares. This must be so because in non-squares, for every divisor greater than the square-root there is a complement smaller than the square-root. But in squares the square-root is its own complement.