Project Euler #23

euler23.py

from math import sqrt

def divisors(n):
    for x in xrange(1, int(sqrt(n)) + 1):
        if n % x == 0:
            yield x
            if x != 1 and x * x != n:
                yield n / x

abundants = set()

def abundantsum(n):
    if sum(divisors(n)) > n:
        abundants.add(n)
    if not any((n - a in abundants) for a in abundants):
        return 0
    return 1

print sum(n for n in range(1, 28124) if not abundantsum(n))