Number properties
=================

The *proper divisors* of an integer number are defined as their positive
divisors except for himself. It is said that a number is *perfect* if
it is equal to the addition of its proper divisors. It is also said that
a number is *deficient* if the addition of its proper divisors is less than
itself, and it is said that it is *abundant* if this addition is greater than
the number itself.

Save all functions into a file named ``properties.py``.

#. Write the function :py:func:`divisors` that given an integer
   number, returns the addition of its proper divisors. Examples:
   
   .. literalinclude:: divisors.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`divisors.txt <divisors.txt>`

#. Write the function :py:func:`number_type` that given an integer
   number, returns a string with the values ``'abundant'``,
   ``'deficient'`` or ``'perfect'`` depending on which of these types
   the given number is. This function must call the previous function
   :py:func:`divisors`. Examples:
   
   .. literalinclude:: properties-1.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`properties-1.txt <properties-1.txt>`

#. Is is said that two integer numbers *n* and *m* are *friends* if
   the addition of the proper divisors of *n* is *m* and the addition of the
   proper divisors of *m* is *n*. Write the Boolean function
   :py:func:`are_friends` that, given two integers, returns ``True``
   if they are friends and ``False`` otherwise.  This function must
   call the previous function :py:func:`divisors`. Examples:
   
      .. literalinclude:: properties-2.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`properties-2.txt <properties-2.txt>`

.. rubric:: Solution

A solution of these functions is provided in file :download:`properties.py <solutions/properties.py>`