Python Challenges: Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers

Python Challenges - 1: Exercise-47 with Solution

Write a Python program to find the sum of all the positive integers which cannot be written as the sum of two abundant numbers.

From Wikipedia - Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number. (A proper divisor of a number is a positive factor of that number other than the number itself. For example, the proper divisors of 6 are 1, 2, and 3.)
The smallest pair of amicable numbers is (220, 284). They are amicable because the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, of which the sum is 284; and the proper divisors of 284 are 1, 2, 4, 71 and 142, of which the sum is 220.

Sample Solution:

Python Code:

from functools import reduce
from itertools import combinations_with_replacement as combinations
MAX_NUM = 28123

def divisors(x):
    return set(reduce(list.__add__, [[div, x//div] for div in range(2, int(x**0.5) + 1) if x % div == 0] + [[1]]))

def abundant(nums):
    return sum(divisors(nums)) > nums

abundant_nums = (n for n in range(1, MAX_NUM) if abundant(n))
sum_of_two_abundants = set(a + b for a, b in combinations(abundant_nums, 2))
not_abundant_nums = (x for x in range(MAX_NUM) if x not in sum_of_two_abundants)
print(sum(not_abundant_nums))

Sample Output:

4179871

Flowchart:

Python Code Editor:

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