From 5354d2a1815e6382c50ed9cca883c01585d0c8dc Mon Sep 17 00:00:00 2001
From: Franz Diebold <franz.diebold@tum.de>
Date: Thu, 3 Oct 2019 09:47:18 +0200
Subject: [PATCH] Add solution for problem 21.

---
 README.md                    |  2 +-
 src/p021_amicable_numbers.py | 62 ++++++++++++++++++++++++++++++++++++
 2 files changed, 63 insertions(+), 1 deletion(-)
 create mode 100644 src/p021_amicable_numbers.py

diff --git a/README.md b/README.md
index c36adbb..8d63b2b 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # [Project Euler](https://projecteuler.net) Solutions
 
-[![solved: 20 problems](https://img.shields.io/badge/solved-20_problems-f93.svg)](./src)
+[![solved: 21 problems](https://img.shields.io/badge/solved-21_problems-f93.svg)](./src)
 ![Python: 3.7](https://img.shields.io/badge/Python-3.7-3776ab.svg)
 [![Build Status](https://travis-ci.com/FranzDiebold/project-euler-solutions.svg?branch=master)](https://travis-ci.com/FranzDiebold/project-euler-solutions)
 [![license: MIT](https://img.shields.io/badge/license-MIT-brightgreen.svg)](./LICENSE.md)
diff --git a/src/p021_amicable_numbers.py b/src/p021_amicable_numbers.py
new file mode 100644
index 0000000..a81fb10
--- /dev/null
+++ b/src/p021_amicable_numbers.py
@@ -0,0 +1,62 @@
+"""
+Problem 21: Amicable numbers
+https://projecteuler.net/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.
+"""
+
+from typing import Iterable, Tuple
+import math
+
+
+def divisors(number: int) -> Iterable[int]:
+    """Get proper divisors for given number `number`.
+
+    Example:
+    220 -> [1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110]
+    The numbers may be in a random order.
+    """
+    yield 1
+    for i in range(2, math.floor(math.sqrt(number))):
+        if number % i == 0:
+            yield i
+            yield number // i
+
+
+def get_sum_of_divisors(number: int) -> int:
+    """Get sum of proper divisors of number `number`."""
+    return sum(divisors(number))
+
+
+def get_amicable_pairs(threshold: int) -> Iterable[Tuple[int, int]]:
+    """Get amicable number pairs (as tuples) up to a threshold."""
+    number_to_sum_divisors = {}
+    for i in range(1, threshold):
+        sum_of_divisors = get_sum_of_divisors(i)
+        if number_to_sum_divisors.get(sum_of_divisors) == i:
+            yield (sum_of_divisors, i)
+        number_to_sum_divisors[i] = sum_of_divisors
+
+
+def main() -> None:
+    """Main function."""
+    threshold = 10000
+    sum_of_amicable_numbers = 0
+    # pylint: disable=invalid-name
+    for (a, b) in get_amicable_pairs(threshold):
+        sum_of_amicable_numbers += a + b
+    print(f'The sum of all the amicable numbers under {threshold:,} ' \
+          f'is {sum_of_amicable_numbers:,}.')
+
+
+if __name__ == '__main__':
+    main()