Refactor with itertools

src/project_euler_python/problems_001_050/Problem023.py

@@ -9,9 +9,21 @@ Solution for problem 023 of Project Euler
 https://projecteuler.net/problem=23
 """
 
+from itertools import combinations_with_replacement
+
 from project_euler_python.utils import timeit
 
 
+def _get_abundant_numbers(limit):
+    divisor_sums = [0 for _ in range(limit)]
+
+    for divisor in range(1, limit):
+        for multiple in range(divisor * 2, limit, divisor):
+            divisor_sums[multiple] += divisor
+
+    return [number for number in range(1, limit) if divisor_sums[number] > number]
+
+
 @timeit("Problem 023")
 def compute():
     """
@@ -35,25 +47,19 @@ def compute():
     sum of two abundant numbers.
     """
 
-    limit = 28124
-    divisor_sum = [0] * limit
-    for i in range(1, limit):
-        for j in range(i * 2, limit, i):
-            divisor_sum[j] += i
+    limit = 28123 + 1
+    abundant_numbers = _get_abundant_numbers(limit)
 
-    abundant_nums = [i for (i, x) in enumerate(divisor_sum) if x > i]
+    expressible_sums = {
+        first + second
+        for first, second in combinations_with_replacement(
+            abundant_numbers,
+            2,
+        )
+        if first + second < limit
+    }
 
-    expressible = [False] * limit
-    for i in abundant_nums:
-        for j in abundant_nums:
-            if i + j < limit:
-                expressible[i + j] = True
-            else:
-                break
-
-    ans = sum(i for (i, x) in enumerate(expressible) if not x)
-
-    return ans
+    return sum(number for number in range(1, limit) if number not in expressible_sums)
 
 
 if __name__ == "__main__":