perfect

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Perfect Numbers

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 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.

Implementation

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.

Running the tests

To run the tests run the command go test from within the exercise directory.

If the test suite contains benchmarks, you can run these with the -bench flag:

go test -bench .

Keep in mind that each reviewer will run benchmarks on a different machine, with different specs, so the results from these benchmark tests may vary.

Further information

For more detailed information about the Go track, including how to get help if you're having trouble, please visit the exercism.io Go language page.

Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

Documentation

Index

• Variables
• type Classification
  • func Classify(n int64) (Classification, error)

Variables

var (
	ErrOnlyPositive = errors.New("Positive number is required")
)

Errors

Types

type Classification

type Classification string

Classification is the category devised by Greek Mathematician Nicomachus�

const (
	ClassificationDeficient Classification = "deficient"
	ClassificationPerfect   Classification = "perfect"
	ClassificationAbundant  Classification = "abundant"
)

Defined categories

func Classify

func Classify(n int64) (Classification, error)

Classify finds the category of given natural number