The Greek mathematican Nicomachus devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of abundant, perfect, or deficient. A perfect number equals the sum of its positive divisors — the pairs of numbers whose product yields the target number, excluding the number itself.

• Perfect: Sum of factors = number
• Abundant: Sum of factors > number
• Deficient: Sum of factors < number

The Aliquot sum is defined as the sum of the factors of a number not including the number itself.

Examples

• 6 is a perfect number because its divisors are 1, 2, 3 and 6 = 1 + 2 + 3.
• 28 is perfect number because 28 = 1 + 2 + 4 + 7 + 14.
• Prime numbers 7, 13, etc are Deficient by the Nicomachus classificaton.