# Euler Solution 23

### From ProgSoc Wiki

Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

# Solutions to Problem 23

## Python by Althalus

Runtime:171 seconds

from math import sqrt def getFactors(num): list = [1,] for i in range(2,int(sqrt(num)+1)): if num%i == 0: list.append(i) #Added this if statement to handle squares. #EG, i was getting the factors of 4 = 1,2,2 #hence 4 was incorrectly being reported as abundant. if num/i not in list: list.append(num/i) return list def isAbundant(num): if sum(getFactors(num)) > num: return True return False abundants = [] for i in range(1,28124): if isAbundant(i): abundants.append(i) total=0 for i in range(1,28124): sum_of_abundants = False for n in abundants: if i-n <= 0: break elif isAbundant(i-n): sum_of_abundants = True break if sum_of_abundants == False: total+=i print (total)