def eul32():
""""Find the sum of all products whose multiplicand/multiplier/product identity can be written as a
1 through 9 pandigital."""
products = set()
for product in range(1000, 10000):
if len(set(eul.get_digits(product))) == len(str(product)):
for i in eul.get_proper_divisors(product):
j = int(product / i)
test = ''.join([str(i), str(j), str(i*j)])
if len(test) == 9 and eul.pandigital(test):
products.add(i*j)
return sum(products)
def eul23():
"""Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers."""
upper = 28123
abundants = set([x for x in range(12, upper) if sum(eul.get_proper_divisors(x)) > x])
abundant_sums = set([(i + j) for i in abundants for j in abundants if i+j < upper])
return sum(set([x for x in range(1, upper)]) - abundant_sums)
def eul21():
"""Evaluate the sum of all the amicable numbers under 10000."""
return sum([x for x in range(1, 10000) if
x != sum(eul.get_proper_divisors(x)) and sum(
eul.get_proper_divisors(sum(eul.get_proper_divisors(x)))) == x])
