Sum all amicable numbers from 1 to specified numbersΒΆ

Sum all amicable numbers from 1 to specified numbers.
Note:
Amicable numbers are two different numbers so related that the sum
of the proper divisors of each is equal to the other number.
(A proper divisor of a number is a positive factor of that number
other than the number itself.
For example, the proper divisors of 6 are 1, 2, and 3.)
Test Data:
amicable_numbers_sum(9999)
amicable_numbers_sum(999)
amicable_numbers_sum(99)
Expected output:
31626
504
0
def amicable_numbers_sum(limit):

    if not isinstance(limit, int):
        return "Input is not an integer!"

    if limit < 1:
        return "Input must be bigger than 0!"

    amicables = set()

    for num in range(2, limit+1):
        if num in amicables:
            continue

        sum_fact  = sum([fact for fact in range(1, num) if num % fact == 0])
        sum_fact2 = sum([fact for fact in range(1, sum_fact) if sum_fact % fact == 0])

    if num == sum_fact2 and num != sum_fact:
        amicables.add(num)
        amicables.add(sum_fact2)

    return sum(amicables)

# test
print(amicable_numbers_sum(9999))
print(amicable_numbers_sum(999))
print(amicable_numbers_sum(99))

Output:

31626
504
0