Check if the given number is Ore number or not (original) (raw)

Last Updated : 11 Jul, 2025

Given a positive integer n, check if it is an Ore number or not. Print 'YES' if n is an ore number otherwise print 'NO'.
Ore Number: In mathematics, Ore numbers are positive integers whose divisors have an integer harmonic value. Ore numbers are often called harmonic divisor numbers. Ore numbers are named after Øystein Ore.
For example, 6 has four divisors namely 1, 2, 3, and 6.
The harmonic mean of the divisors is-

The harmonic mean of divisors of 6 is 2, an integer. So, 6 is an Ore number or harmonic divisor number.
First, a few Ore numbers or harmonic divisor numbers are:

1, 6, 28, 140, 270, 496, 672, 1638, 2970, 6200, 8128, 8190

Examples:

Input : N = 6 Output : Yes

Input : N = 4 Output: No Explanation : Harmonic mean of divisors of 4 is not an Integer.

Prerequisite:

• Harmonic Mean
• How to Generate all Divisors of a number

The idea is to generate all divisors of the given number and then check if the harmonic mean of the divisor is an Integer or not.

1. Generate All Divisors of the given number - 'n'
2. Calculate the Harmonic mean of the divisors of n
3. Check if the Harmonic mean is an Integer or not
4. If Yes, Then the number is an Ore Number otherwise Not

Below is the implementation of the above approach:

C++ `

// CPP program to check if the given number is // Ore number

#include <bits/stdc++.h> using namespace std;

vector arr;

// Function that returns harmonic mean void generateDivisors(int n) { // Note that this loop runs till square root for (int i = 1; i <= sqrt(n); i++) { if (n % i == 0) {

        // If divisors are equal, store 'i'
        if (n / i == i)
            arr.push_back(i);

        else // Otherwise store 'i' and 'n/i' both
        {
            arr.push_back(i);
            arr.push_back(n / i);
        }
    }
}

}

// Utility function to calculate harmonic // mean of the divisors double harmonicMean(int n) { generateDivisors(n);

// Declare sum variables and initialize
// with zero.

double sum = 0.0;

int len = arr.size();

// calculate denominator
for (int i = 0; i < len; i++)
    sum = sum + double(n / arr[i]);

sum = double(sum / n);

// Calculate harmonic mean and return

return double(arr.size() / sum);

}

// Function to check if a number is ore number bool isOreNumber(int n) { // Calculate Harmonic mean of divisors of n double mean = harmonicMean(n);

// Check if harmonic mean is an integer or not
if (mean - int(mean) == 0)
    return true;
else
    return false;

}

// Driver Code int main() { int n = 28;

if (isOreNumber(n))
    cout << "YES";
else
    cout << "NO";

return 0;

}

Java

// Java program to check if the given // number is Ore number

import java.util.*; class GFG {

static Vector<Integer> arr = new Vector<Integer>();

// Function that returns harmonic mean.
static void generateDivisors(int n)
{
    // Note that this loop runs till square root
    for (int i = 1; i <= Math.sqrt(n); i++) {
        if (n % i == 0) {

            // If divisors are equal, store 'i'
            if (n / i == i)
                arr.add(i);

            else // Otherwise store 'i' and 'n/i' both
            {
                arr.add(i);
                arr.add(n / i);
            }
        }
    }
}

// Utility function to calculate harmonic mean
// of the divisors
static double harmonicMean(int n)
{
    generateDivisors(n);

    // Declare sum variables and initialize
    // with zero.

    double sum = 0.0;

    int len = arr.size();

    // calculate denominator
    for (int i = 0; i < len; i++)
        sum = sum + n / arr.get(i);

    sum = sum / n;

    // Calculate harmonic mean and return

    return arr.size() / sum;
}

// Function to check if a number
// is Ore number
static boolean isOreNumber(int n)
{
    // Calculate Harmonic mean of divisors of n
    double mean = harmonicMean(n);

    // Check if Harmonic mean is an Integer or not
    if (mean - Math.floor(mean) == 0)
        return true;
    else
        return false;
}

// Driver Code
public static void main(String[] args)
{
    int n = 28;

    if (isOreNumber(n))
        System.out.println("YES");
    else
        System.out.println("NO");
}

}

Python3

Python3 program to check if the

given number is Ore number

arr = []

Function that returns harmonic mean

def generateDivisors(n):

# Note that this loop runs till square root 
for i in range(1, int(n**(0.5)) + 1): 
    if n % i == 0:

        # If divisors are equal, store 'i' 
        if n // i == i: 
            arr.append(i) 
        
        # Otherwise store 'i' and 'n/i' both
        else: 
            arr.append(i) 
            arr.append(n // i) 
    

Utility function to calculate harmonic

mean of the divisors

def harmonicMean(n):

generateDivisors(n) 

# Declare sum variables and initialize 
# with zero. 
Sum = 0
length = len(arr) 

# calculate denominator 
for i in range(0, length): 
    Sum = Sum + (n / arr[i]) 

Sum = Sum / n 

# Calculate harmonic mean and return 
return length / Sum

Function to check if a number

is ore number

def isOreNumber(n):

# Calculate Harmonic mean of 
# divisors of n 
mean = harmonicMean(n) 

# Check if harmonic mean is an 
# integer or not 
if mean - int(mean) == 0: 
    return True
else:
    return False

Driver Code

if name == "main":

n = 28

if isOreNumber(n) == True: 
    print("YES") 
else:
    print("NO") 

This code is contributed

by Rituraj Jain

C#

// C# program to check if the given // number is Ore number using System; using System.Collections;

class GFG {

static ArrayList arr = new ArrayList();

// Function that returns harmonic mean. static void generateDivisors(int n) { // Note that this loop runs // till square root for (int i = 1; i <= Math.Sqrt(n); i++) { if (n % i == 0) {

        // If divisors are equal, 
        // store 'i'
        if (n / i == i)
            arr.Add(i);

        else // Otherwise store 'i' 
             // and 'n/i' both
        {
            arr.Add(i);
            arr.Add(n / i);
        }
    }
}

}

// Utility function to calculate // harmonic mean of the divisors static double harmonicMean(int n) { generateDivisors(n);

// Declare sum variables and 
// initialize with zero.
double sum = 0.0;

int len = arr.Count;

// calculate denominator
for (int i = 0; i < len; i++)
    sum = sum + n / (int)arr[i];

sum = sum / n;

// Calculate harmonic mean 
// and return
return arr.Count / sum;

}

// Function to check if a number // is Ore number static bool isOreNumber(int n) { // Calculate Harmonic mean of // divisors of n double mean = harmonicMean(n);

// Check if Harmonic mean is 
// an Integer or not
if (mean - Math.Floor(mean) == 0)
    return true;
else
    return false;

}

// Driver Code public static void Main() { int n = 28;

if (isOreNumber(n))
    Console.WriteLine("YES");
else
    Console.WriteLine("NO");

} }

// This code is contributed by mits

JavaScript

`

Time Complexity: O(sqrt(n)), Where n is the given number.
Auxiliary Space: O(sqrt(n)), for storing the divisor of n in the array