def euler_23():
"""Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers."""
from eutil import divisors
abundants = set([n for n in range(1, 20162) if sum(sorted(divisors(n))[:-1]) > n])
return sum(n for n in range(1, 20162) if not any(((n - a) in abundants) for a in abundants))
def euler_12():
"""What is the value of the first triangle number to have over five hundred divisors?"""
from itertools import dropwhile
from eutil import triangle_numbers, divisors
return next(dropwhile(lambda x: len(divisors(x)) < 500, triangle_numbers()))
def d(n):
return sum(sorted(divisors(n))[:-1])