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

Last update on April 24 2025 12:35:20 (UTC/GMT +8 hours)

14. Amicable Numbers Sum

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

Pictorial Presentation:

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to calculate the sum of proper divisors for a given number and then determine if it is amicable with any other number in a specified range.
• Write a Python function that accepts a number and returns the sum of its amicable pair if it exists, or 0 if not.
• Write a Python script to iterate through a list of numbers and print the amicable pair sums for each number that forms an amicable pair.
• Write a Python program to check if a number has an amicable pair by comparing its proper divisor sum to another number's divisor sum, and then print the amicable pair if found.

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