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rootulp's solution

to Perfect Numbers in the Python Track

Published at Jul 13 2018 · 0 comments
Test suite


This solution was written on an old version of Exercism. The tests below might not correspond to the solution code, and the exercise may have changed since this code was written.

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.

Exception messages

Sometimes it is necessary to raise an exception. When you do this, you should include a meaningful error message to indicate what the source of the error is. This makes your code more readable and helps significantly with debugging. Not every exercise will require you to raise an exception, but for those that do, the tests will only pass if you include a message.

To raise a message with an exception, just write it as an argument to the exception type. For example, instead of raise Exception, you should write:

raise Exception("Meaningful message indicating the source of the error")

Running the tests

To run the tests, run the appropriate command below (why they are different):

  • Python 2.7: py.test perfect_numbers_test.py
  • Python 3.4+: pytest perfect_numbers_test.py

Alternatively, you can tell Python to run the pytest module (allowing the same command to be used regardless of Python version): python -m pytest perfect_numbers_test.py

Common pytest options

  • -v : enable verbose output
  • -x : stop running tests on first failure
  • --ff : run failures from previous test before running other test cases

For other options, see python -m pytest -h

Submitting Exercises

Note that, when trying to submit an exercise, make sure the solution is in the $EXERCISM_WORKSPACE/python/perfect-numbers directory.

You can find your Exercism workspace by running exercism debug and looking for the line that starts with Workspace.

For more detailed information about running tests, code style and linting, please see the help page.


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.


import unittest

from perfect_numbers import classify

# Tests adapted from `problem-specifications//canonical-data.json` @ v1.1.0

class PerfectNumbersTest(unittest.TestCase):
    def test_smallest_perfect_number(self):
        self.assertIs(classify(6), "perfect")

    def test_medium_perfect_number(self):
        self.assertIs(classify(28), "perfect")

    def test_large_perfect_number(self):
        self.assertIs(classify(33550336), "perfect")

class AbundantNumbersTest(unittest.TestCase):
    def test_smallest_abundant_number(self):
        self.assertIs(classify(12), "abundant")

    def test_medium_abundant_number(self):
        self.assertIs(classify(30), "abundant")

    def test_large_abundant_number(self):
        self.assertIs(classify(33550335), "abundant")

class DeficientNumbersTest(unittest.TestCase):
    def test_smallest_prime_deficient_number(self):
        self.assertIs(classify(2), "deficient")

    def test_smallest_nonprime_deficient_number(self):
        self.assertIs(classify(4), "deficient")

    def test_medium_deficient_number(self):
        self.assertIs(classify(32), "deficient")

    def test_large_deficient_number(self):
        self.assertIs(classify(33550337), "deficient")

    def test_edge_case(self):
        self.assertIs(classify(1), "deficient")

class InvalidInputsTest(unittest.TestCase):
    def test_zero(self):
        with self.assertRaisesWithMessage(ValueError):

    def test_negative(self):
        with self.assertRaisesWithMessage(ValueError):

    # Utility functions
    def setUp(self):
        except AttributeError:
            self.assertRaisesRegex = self.assertRaisesRegexp

    def assertRaisesWithMessage(self, exception):
        return self.assertRaisesRegex(exception, r".+")

if __name__ == '__main__':
import math

def is_perfect(number):
    return sum(factors(number)) == number

def factors(n):
    return set(reduce(list.__add__, pairs_of_factors(n))) - set([n])

def pairs_of_factors(n):
    return [[i, n / i] for i in xrange(1, int(math.sqrt(n)) + 1) if n % i == 0]

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