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The positive divisors of a number that are less than the number itself are called proper divisors. For example, 1 and 2 are the only proper divisors of 4. The ancient Greeks classified natural numbers as deficient, perfect, or abundant, depending on the sum of their proper divisors. It turns out that the perfect numbers occur much less frequently than the others. However, as early as 500 BC, the first three perfect numbers were known.
A number is deficient if the sum of its proper divisors is less than the number itself.
A number is abundant if the sum of its proper divisors is greater than the number itself.
A number is perfect if the sum of its proper divisors is equal to the number itself.
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