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Add function to check deficient numbers (#13528)
* Add function to check deficient numbers Introduces is_deficient_number to determine if a number is deficient by comparing the sum of its proper divisors to the number itself. Includes input validation and doctests for correctness. * updating DIRECTORY.md * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update deficient_numbers.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update deficient_numbers.py Fixed code issue * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * updating DIRECTORY.md * Add docstring for deficient number explanation Added a docstring explaining deficient numbers and provided examples. --------- Co-authored-by: ArunKishoreVoleti <ArunKishoreVoleti@users.noreply.github.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: cclauss <cclauss@users.noreply.github.com>
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‎DIRECTORY.md‎

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* [Bell Numbers](maths/special_numbers/bell_numbers.py)
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* [Carmichael Number](maths/special_numbers/carmichael_number.py)
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* [Catalan Number](maths/special_numbers/catalan_number.py)
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* [Deficient Numbers](maths/special_numbers/deficient_numbers.py)
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* [Disarum Number](maths/special_numbers/disarum_number.py)
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* [Hamming Numbers](maths/special_numbers/hamming_numbers.py)
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* [Happy Number](maths/special_numbers/happy_number.py)

‎maths/special_numbers/deficient_numbers.py‎

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"""
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A number n is said to be a Deficient number if
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the sum of its proper divisors is less than the number itself.
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Examples of Deficient Numbers: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, ...
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https://en.wikipedia.org/wiki/Deficient_number
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"""
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def is_deficient_number(number: int) -> bool:
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"""
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This function takes an integer number as input.
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Returns True if the number is a deficient number.
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>>> is_deficient_number(-1)
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False
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>>> is_deficient_number(0)
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False
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>>> is_deficient_number(1)
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True
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>>> is_deficient_number(2)
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True
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>>> is_deficient_number(6)
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False
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>>> is_deficient_number(12)
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False
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>>> is_deficient_number(7)
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True
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>>> is_deficient_number(28)
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False
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>>> is_deficient_number(15)
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True
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>>> is_deficient_number(8.0)
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Traceback (most recent call last):
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...
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TypeError: Input value of [number=8.0] must be an integer
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"""
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if not isinstance(number, int):
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msg = f"Input value of [number={number}] must be an integer"
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raise TypeError(msg)
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if number < 1:
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return False
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if number == 1:
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return True
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divisor_sum = 1
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for i in range(2, int(number**0.5) + 1):
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if number % i == 0:
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divisor_sum += i
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if i != number // i:
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divisor_sum += number // i
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return divisor_sum < number
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if __name__ == "__main__":
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import doctest
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doctest.testmod()

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