Add solution for problem 23.

README.md

@@ -1,6 +1,6 @@
 # [Project Euler](https://projecteuler.net) Solutions
 
-[![solved: 22 problems](https://img.shields.io/badge/solved-22_problems-f93.svg)](./src)
+[![solved: 23 problems](https://img.shields.io/badge/solved-23_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)

src/common/divisors.py

@@ -0,0 +1,54 @@
+"""
+Proper divisor utility functions.
+"""
+
+from typing import Iterable
+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)) + 1):
+        if number % i == 0:
+            yield i
+            if i**2 < number:
+                yield number // i
+
+
+def get_sum_of_divisors(number: int) -> int:
+    """Get sum of proper divisors of number `number`."""
+    return sum(divisors(number))
+
+
+def is_perferct_number(number: int) -> bool:
+    """Check if a given number `number` is a perfect number.
+
+    A perfect number is a number for which the sum of its proper divisors
+    is exactly equal to the number.
+    For example, the sum of the proper divisors of 28 would be
+        `1 + 2 + 4 + 7 + 14 = 28`,
+    which means that 28 is a perfect number.
+    """
+    return get_sum_of_divisors(number) == number
+
+
+def is_deficient_number(number: int) -> bool:
+    """Check if a given number `number` is a deficient number.
+
+    A number n is called deficient if the sum of its proper divisors is less than n.
+    """
+    return get_sum_of_divisors(number) < number
+
+
+def is_abundant_number(number: int) -> bool:
+    """Check if a given number `number` is a abundant number.
+
+    A number n is called abundant if the sum of its proper divisors exceeds n.
+    """
+    return get_sum_of_divisors(number) > number

src/p021_amicable_numbers.py

@@ -15,26 +15,8 @@
 """
 
 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))
+from src.common.divisors import get_sum_of_divisors
 
 
 def get_amicable_pairs(threshold: int) -> Iterable[Tuple[int, int]]:

src/p023_non_abundant_sums.py

@@ -0,0 +1,61 @@
+"""
+Problem 23: Non-abundant sums
+https://projecteuler.net/problem=23
+
+A perfect number is a number for which the sum of its proper divisors
+is exactly equal to the number.
+For example, the sum of the proper divisors of 28 would be
+1 + 2 + 4 + 7 + 14 = 28,
+which means that 28 is a perfect number.
+
+A number n is called deficient if the sum of its proper divisors is less than n and
+it is called abundant if this sum exceeds n.
+
+As 12 is the smallest abundant number, 1 + 2 + 3 + 4 + 6 = 16,
+the smallest number that can be written as the sum of two abundant numbers is 24.
+By mathematical analysis, it can be shown that all integers greater than 28123
+can be written as the sum of two abundant numbers.
+However, this upper limit cannot be reduced any further by analysis
+even though it is known that the greatest number that cannot be expressed
+as the sum of two abundant numbers is less than this limit.
+
+Find the sum of all the positive integers
+which cannot be written as the sum of two abundant numbers.
+"""
+
+from typing import Set
+
+from src.common.divisors import is_abundant_number
+
+
+def get_abundant_numbers(threshold: int) -> Set[int]:
+    """Get set of abundant numbers below given threshold `threshold'."""
+    abundant_numbers = set()
+    for i in range(1, threshold + 1):
+        if is_abundant_number(i):
+            abundant_numbers.add(i)
+    return abundant_numbers
+
+
+def is_sum_of_numbers(number: int, numbers: Set[int]) -> bool:
+    """Check if a given number `number` is the sum of any two numbers from `numbers`."""
+    for i in range(1, number):
+        if i in numbers and (number - i) in numbers:
+            return True
+    return False
+
+
+def main() -> None:
+    """Main function."""
+    threshold = 28123
+    total_sum = 0
+    abundant_numbers = get_abundant_numbers(threshold)
+    for i in range(1, threshold + 1):
+        if not is_sum_of_numbers(i, abundant_numbers):
+            total_sum += i
+    print(f'The sum of all the positive integers which cannot be written as the sum ' \
+          f'of two abundant numbers is {total_sum:,}.')
+
+
+if __name__ == '__main__':
+    main()