Check if sum of divisors of two numbers are same

Last Updated : 28 Sep, 2018

Given two numbers n1 & n2, We need to check whether these numbers are equivalent numbers or not.
Equivalent numbers are numbers such that the sums of their proper divisors are the same.
For example, 159, 559, and 703 are equivalent numbers. This is because all the three numbers have 57 as the sum of their proper divisors.

Examples :

Input : n1 = 559, n2 = 703
Output : Yes.
Explanation: Both numbers have 57 as a sum of their proper divisors.

Input : n1 = 36, n2 = 57
Output : No.
Explanation: 36 has sum 55 while 57 has sum 23 of their proper divisors.

Find the sum of proper divisors as implemented in for Perfect number for the given numbers and then will check if both sums are equal or not.

C++

// C++ program to find if two numbers are 
// equivalent or not 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to calculate sum of all proper divisors 
// num --> given natural number 
int divSum(int n) 
{ 
    // To store sum of divisors 
    long long int sum = 1; 
  
    // Find all divisors and add them 
    for (long long int i = 2; i * i <= n; i++) 
        if (n % i == 0) 
            sum = sum + i + n / i; 
  
    return sum; 
} 
  
// Function to check if both numbers 
// are equivalent or not 
bool areEquivalent(int num1, int num2) 
{ 
    return divSum(num1) == divSum(num2); 
} 
  
// Drivers code 
int main() 
{ 
    int num1 = 559, num2 = 703; 
  
    areEquivalent(num1, num2) ?  
                  cout << "Equivalent" :  
                  cout << "Not Equivalent"; 
  
    return 0; 
} 

Java

// Java program to find if two numbers are 
// equivalent or not 
import java.math.*; 
  
class GFG { 
  
    // Function to calculate sum of all proper 
    // divisors num --> given natural number 
    static int divSum(int n) 
    { 
        // To store sum of divisors 
        int sum = 1; 
  
        // Find all divisors and add them 
        for (int i = 2; i * i <= n; i++) 
            if (n % i == 0) 
                sum = sum + i + n / i; 
  
        return sum; 
    } 
  
    // Function to check if both numbers 
    // are equivalent or not 
    static boolean areEquivalent(int num1, int num2) 
    { 
  
        return divSum(num1) == divSum(num2); 
    } 
  
    // Drivers code 
    public static void main(String[] args) 
    { 
        int num1 = 559; 
        int num2 = 703; 
  
        if (areEquivalent(num1, num2)) 
            System.out.println("Equivalent"); 
        else
            System.out.println("Not Equivalent"); 
    } 
} 

Python3

# Python3 program to find  
# if two numbers are 
# equivalent or not 
import math 
  
# Function to calculate sum  
# of all proper divisors 
# num --> given natural number 
def divSum(n): 
      
    # To store sum of divisors 
    sum = 1; 
  
    # Find all divisors 
    # and add them 
    i = 2; 
    while(i * i <= n): 
        if (n % i == 0): 
            sum = (sum + i +
                   math.floor(n / i)); 
        i += 1; 
  
    return sum; 
  
# Function to check  
# if both numbers 
# are equivalent or not 
def areEquivalent(num1, num2): 
    return divSum(num1) == divSum(num2); 
  
# Driver code 
num1 = 559;  
num2 = 703; 
  
if (areEquivalent(num1, num2) == True): 
    print("Equivalent"); 
else: 
    print("Not Equivalent"); 
              
# This code is contributed by mits 

C#

// C# program to find if two  
// numbers are equivalent or not 
using System; 
  
class GFG 
{ 
      
    // Function to calculate sum  
    // of all proper divisors  
    // num --> given natural number 
    static int divSum(int n) 
    { 
        // To store sum of divisors 
        int sum = 1; 
  
        // Find all divisors 
        // and add them 
        for (int i = 2; i * i <= n; i++) 
            if (n % i == 0) 
                sum = sum + i + n / i; 
  
        return sum; 
    } 
  
    // Function to check if  
    // both numbers are  
    // equivalent or not 
    static bool areEquivalent(int num1,  
                              int num2) 
    { 
        return divSum(num1) == divSum(num2); 
    } 
  
    // Driver code 
    static public void Main () 
    { 
        int num1 = 559; 
        int num2 = 703; 
  
        if (areEquivalent(num1, num2)) 
            Console.WriteLine("Equivalent"); 
        else
            Console.WriteLine("Not Equivalent"); 
    } 
} 
  
// This code is contributed by m_kit 

PHP

<?php 
// PHP program to find  
// if two numbers are 
// equivalent or not 
  
// Function to calculate sum  
// of all proper divisors 
// num --> given natural number 
function divSum($n) 
{ 
    // To store sum of divisors 
    $sum = 1; 
  
    // Find all divisors 
    // and add them 
    for ($i = 2; $i * $i <= $n; $i++) 
        if ($n % $i == 0) 
            $sum = $sum + $i +  
                   floor($n / $i); 
  
    return $sum; 
} 
  
// Function to check  
// if both numbers 
// are equivalent or not 
function areEquivalent($num1, $num2) 
{ 
    return divSum($num1) == divSum($num2); 
} 
  
// Driver code 
$num1 = 559; $num2 = 703; 
  
if (areEquivalent($num1, $num2) == true)  
    echo "Equivalent" ; 
              
else
    echo "Not Equivalent"; 
              
// This code is contributed by ajit 
?> 

Output:

Equivalent

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