Perfect Numbers

Instructions

Determine if a number is perfect, abundant, or deficient based on Nicomachus' (60 - 120 CE) classification scheme for positive integers.

The Greek mathematician Nicomachus devised a classification scheme for positive integers, 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 way to determine whether a given number is perfect. Depending on your language track, you may also need to implement a way to determine whether a given number is abundant or deficient.

Define type Classification for containing the classification values for natural numbers. You may choose any representation for this type.

Define three Classification constants named

	ClassificationDeficient
	ClassificationPerfect
	ClassificationAbundant

Implement a function named Classify which accepts an int64 input and returns a Classification and an error value.

Create an error named ErrOnlyPositive which is returned when the input is not a positive integer.

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Source

Taken from Chapter 2 of Functional Thinking by Neal Ford.