def problem23():
""" Non-abundant sums
Find the sum of all the positive integers which cannot be written
as the sum of two abundant numbers.
"""
abundants = [x for x in range(1, 28124) if mathhelper.sum_factors(x, proper=True) > x]
abundants_sum = {x + y for (x, y) in itertools.product(abundants, repeat=2) if x + y < 28124}
return sum(x for x in range(1, 28124) if x not in abundants_sum)
def test_sum_factors(self):
self.assertEqual(mathhelper.sum_factors(-1), 1)
self.assertEqual(mathhelper.sum_factors(0), 0)
self.assertEqual(mathhelper.sum_factors(1), 1)
self.assertEqual(mathhelper.sum_factors(2), 3)
self.assertEqual(mathhelper.sum_factors(3), 4)
self.assertEqual(mathhelper.sum_factors(4), 7)
self.assertEqual(mathhelper.sum_factors(5), 6)
self.assertEqual(mathhelper.sum_factors(6), 12)
self.assertEqual(mathhelper.sum_factors(10), 18)
self.assertEqual(mathhelper.sum_factors(12), 28)
self.assertEqual(mathhelper.sum_factors(25), 31)
self.assertEqual(mathhelper.sum_factors(-1, True), 0)
self.assertEqual(mathhelper.sum_factors(0, True), 0)
self.assertEqual(mathhelper.sum_factors(1, True), 0)
self.assertEqual(mathhelper.sum_factors(2, True), 1)
self.assertEqual(mathhelper.sum_factors(3, True), 1)
self.assertEqual(mathhelper.sum_factors(4, True), 3)
self.assertEqual(mathhelper.sum_factors(5, True), 1)
self.assertEqual(mathhelper.sum_factors(6, True), 6)
self.assertEqual(mathhelper.sum_factors(10, True), 8)
self.assertEqual(mathhelper.sum_factors(12, True), 16)
self.assertEqual(mathhelper.sum_factors(25, True), 6)