project_euler.problem_021.sol1
==============================

.. py:module:: project_euler.problem_021.sol1

.. autoapi-nested-parse::

   Amicable Numbers
   Problem 21

   Let d(n) be defined as the sum of proper divisors of n (numbers less than n
   which divide evenly into n).
   If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and
   each of a and b are called amicable numbers.

   For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55
   and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and
   142; so d(284) = 220.

   Evaluate the sum of all the amicable numbers under 10000.



Functions
---------

.. autoapisummary::

   project_euler.problem_021.sol1.solution
   project_euler.problem_021.sol1.sum_of_divisors


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

.. py:function:: solution(n: int = 10000) -> int

   Returns the sum of all the amicable numbers under n.

   >>> solution(10000)
   31626
   >>> solution(5000)
   8442
   >>> solution(1000)
   504
   >>> solution(100)
   0
   >>> solution(50)
   0


.. py:function:: sum_of_divisors(n: int) -> int