Python Program to Check If Two Numbers are Amicable Numbers or Not

This Python program checks if two numbers are amicable numbers or not. Amicable numbers are pairs of numbers where the sum of the proper divisors of each number equals the other number.

Amicable numbers are a pair of numbers where the sum of the proper divisors of one number is equal to the other number, and vice versa. In other words, the aliquot sum (the sum of proper divisors excluding the number itself) of one number equals the other number.

Problem Statement

Write a Python program to determine if two numbers are amicable numbers or not. An amicable number is a pair of numbers (num1, num2) where the sum of the proper divisors of num1 equals num2, and the sum of the proper divisors of num2 equals num1.

Python Program to Check If Two Numbers are Amicable Numbers or Not

def get_proper_divisors(n):
    divisors = []
    for i in range(1, n):
        if n % i == 0:
            divisors.append(i)
    return divisors

def are_amicable_numbers(num1, num2):
    divisors_num1 = get_proper_divisors(num1)
    sum_num1 = sum(divisors_num1)

    divisors_num2 = get_proper_divisors(num2)
    sum_num2 = sum(divisors_num2)

    if sum_num1 == num2 and sum_num2 == num1:
        return True
    else:
        return False

# Example usage
num1 = int(input("Enter the first number: "))
num2 = int(input("Enter the second number: "))

if are_amicable_numbers(num1, num2):
    print(f"{num1} and {num2} are amicable numbers.")
else:
    print(f"{num1} and {num2} are not amicable numbers.")

How it Works

1. The program defines a function get_proper_divisors(n) that takes a number n as input and returns a list of its proper divisors. It iterates from 1 to n-1 and checks if n is divisible by the current number. If it is, the current number is added to the list of divisors.
2. The program defines another function are_amicable_numbers(num1, num2) that takes two numbers num1 and num2 as input. Inside this function:
   • It calls the get_proper_divisors() function for num1 and num2 to get their respective lists of proper divisors.
   • It calculates the sum of the proper divisors for num1 and assigns it to sum_num1, and calculates the sum of the proper divisors for num2 and assigns it to sum_num2.
   • It checks if sum_num1 is equal to num2 and sum_num2 is equal to num1. If both conditions are true, it returns True, indicating that the numbers are amicable. Otherwise, it returns False.
3. The program prompts the user to enter two numbers, num1 and num2, using the input() function.
4. It calls the are_amicable_numbers() function with num1 and num2 as arguments to check if they are amicable numbers.
5. If the returned value is True, the program displays a message stating that the numbers are amicable. Otherwise, it displays a message stating that the numbers are not amicable.
6. The program execution ends.

To check if two numbers are amicable, the program calculates the sum of the proper divisors for each number and compares it with the other number. If the sums match for both numbers, they are considered amicable. Otherwise, they are not amicable.

You can run the program and input different pairs of numbers to see if they are amicable or not.

Input/ Output