Classify a number by the sum of its proper divisors and list every perfect number up to a limit.
In number theory, the proper divisors of a number are all of its positive divisors except the number
itself. Their sum s(n) classifies the number: it is perfect when s(n) equals n,
abundant when s(n) is greater than n, and deficient when s(n) is less than n.
Example: the proper divisors of 28 are 1, 2, 4, 7 and 14, which sum to 28, so 28 is a perfect number.
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