Solution to problem 23

src/Python/Problem023.py

@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""
+Created on 05 Jan 2019
+
+@author: David Doblas Jiménez
+@email: daviddoji@pm.me
+
+Solution for problem 23 of Project Euler
+https://projecteuler.net/problem=23
+"""
+
+from utils import timeit
+
+
+@timeit("Problem 23")
+def compute():
+    """
+    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.
+    """
+    LIMIT = 28124
+    divisorsum = [0] * LIMIT
+    for i in range(1, LIMIT):
+        for j in range(i * 2, LIMIT, i):
+            divisorsum[j] += i
+    abundantnums = [i for (i, x) in enumerate(divisorsum) if x > i]
+
+    expressible = [False] * LIMIT
+    for i in abundantnums:
+        for j in abundantnums:
+            if i + j < LIMIT:
+                expressible[i + j] = True
+            else:
+                break
+
+    ans = sum(i for (i, x) in enumerate(expressible) if not x)
+    return ans
+
+
+if __name__ == "__main__":
+
+    print(f"Result for Problem 23: {compute()}")