# Python Math: Sum all amicable numbers from 1 to specified numbers

## Python Math: Exercise-14 with Solution

Write a Python program to 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.)

**Sample Solution** :

**Python Code :**

```
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)
print(amicable_numbers_sum(9999))
print(amicable_numbers_sum(999))
print(amicable_numbers_sum(99))
```

Sample Output:

31626 504 0

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