maths.special_numbers.perfect_number
====================================

.. py:module:: maths.special_numbers.perfect_number

.. autoapi-nested-parse::

   == Perfect Number ==
   In number theory, a perfect number is a positive integer that is equal to the sum of
   its positive divisors, excluding the number itself.
   For example: 6 ==> divisors[1, 2, 3, 6]
       Excluding 6, the sum(divisors) is 1 + 2 + 3 = 6
       So, 6 is a Perfect Number

   Other examples of Perfect Numbers: 28, 486, ...

   https://en.wikipedia.org/wiki/Perfect_number



Attributes
----------

.. autoapisummary::

   maths.special_numbers.perfect_number.number


Functions
---------

.. autoapisummary::

   maths.special_numbers.perfect_number.perfect


Module Contents
---------------

.. py:function:: perfect(number: int) -> bool

   Check if a number is a perfect number.

   A perfect number is a positive integer that is equal to the sum of its proper
   divisors (excluding itself).

   Args:
       number: The number to be checked.

   Returns:
       True if the number is a perfect number, False otherwise.

   Start from 1 because dividing by 0 will raise ZeroDivisionError.
   A number at most can be divisible by the half of the number except the number
   itself. For example, 6 is at most can be divisible by 3 except by 6 itself.

   Examples:
   >>> perfect(27)
   False
   >>> perfect(28)
   True
   >>> perfect(29)
   False
   >>> perfect(6)
   True
   >>> perfect(12)
   False
   >>> perfect(496)
   True
   >>> perfect(8128)
   True
   >>> perfect(0)
   False
   >>> perfect(-1)
   False
   >>> perfect(12.34)
   Traceback (most recent call last):
     ...
   ValueError: number must be an integer
   >>> perfect("Hello")
   Traceback (most recent call last):
     ...
   ValueError: number must be an integer


.. py:data:: number