Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for natural numbers.
The Greek mathematician Nicomachus devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of perfect, abundant, or deficient based on their aliquot sum. The aliquot sum is defined as the sum of the factors of a number not including the number itself. For example, the aliquot sum of 15 is (1 + 3 + 5) = 9
- Perfect: aliquot sum = number
- 6 is a perfect number because (1 + 2 + 3) = 6
- 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
- Abundant: aliquot sum > number
- 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16
- 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36
- Deficient: aliquot sum < number
- 8 is a deficient number because (1 + 2 + 4) = 7
- Prime numbers are deficient
Implement a method to determine whether a given number is perfect, abundant or deficient.
This activity also introduces Enum Types or enums.