def problem21(limit):
all_sum_of_factors = {}
for i in range(2, limit):
all_sum_of_factors[i] = sum(helper.all_factors(i)) - i
summation = 0
for i in range(2, limit):
if all_sum_of_factors.get(all_sum_of_factors[i], 0) == i and all_sum_of_factors[i] != i:
summation += i
return summation
def problem23b():
abundants = []
for i in range(0, 28123):
total = sum(helper.all_factors(i)) - i
if total > i and total <= 28123:
abundants.append(i)
total = 0
abundant_sums = set()
for i in range(len(abundants)):
for j in range(i, len(abundants)):
abundant_sum = abundants[i] + abundants[j]
if abundant_sum <= 28123 and abundant_sum >= 0:
abundant_sums.add(abundant_sum)
total = ((28123 * 28124) / 2) - sum(abundant_sums)
return total
def problem23a():
abundants = []
for i in range(2, 28123):
total = sum(helper.all_factors(i)) - i
if total > i:
abundants.append(i)
total = 0
for i in range(1, 28124):
non_abundant_sum = True
for abundant in abundants:
if abundant > i:
break
elif (i - abundant) in abundants:
non_abundant_sum = False
break
if non_abundant_sum:
total += i
return total
