A number is perfect when the sum of its proper divisors (all divisors except itself) equals the number. For example, 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14.
Collect divisors in pairs. When d divides n, so does n / d. Looping d up to √n finds both members of every pair, but don't add √n twice when n is a perfect square.