Check if a number is Triperfect Number

Given a number . The tasks is to check if the given number is a Triperfect Number.
Triperfect Number: A Number is a Triperfect Number if it is equal to three times the sum of its divisors, that is, 3 times sum of its positive divisors.
Examples:

Input: N = 15
Output: false
Divisors of 15 are 1, 3, 5 and 15. Sum of 
divisors is 24 which is not equal to 3*15 i.e. 45.

Input: N = 120
Output: true
Sum of divisors is 360 i.e. 3*120.
Hence 120 is a triperfect number.

A Simple Solution is to go through every number from 1 to N and check if it is a divisor. Maintain sum of all divisors. If sum becomes equal to 3*N, then return true, else return false.
An Efficient Solution is to go through numbers till square root of N. If a number ‘i’ divides n, then add both ‘i’ and n/i to sum.
Below is the implementation of the efficient approach: 

C++

// CPP code to check if a given
// number is Triperfect or not
#include<bits/stdc++.h>
using namespace std;

// Returns true if n is Triperfect
bool isTriPerfect(int n )
{
    // To store sum of divisors.
    // Adding 1 and n since they are divisors of n.
    int sum = 1 + n;

    // Find all divisors and add them
    int i = 2;
    while (i * i <= n)
    {
    if (n % i == 0)
        {
            if (n / i == i)
                sum = sum + i;
            else
                sum = sum + i + n / i;
        }
        i += 1;
    }

    // If sum of divisors is equal to
    // 3 * n, then n is a Triperfect number
    if (sum == 3 * n and n != 1)
       return true;
    else
       false;
}

// Driver program
int main()
{
 int n = 120;

 if (isTriPerfect(n))
    cout<<n<<" is a Triperfect number";
}

//This code is contributed by
// Surendra_Gangwar

Java

// Java code to check if a given
// number is Triperfect or not

public class GFG{

    // Returns true if n is Triperfect
    static boolean isTriPerfect(int n )
    {
        // To store sum of divisors.
        // Adding 1 and n since they are divisors of n.
        int sum = 1 + n;

        // Find all divisors and add them
        int i = 2;
        while (i * i <= n)
        {
        if (n % i == 0)
            {
                if (n / i == i)
                    sum = sum + i;
                else
                    sum = sum + i + n / i;
            }
            i += 1;
        }

        // If sum of divisors is equal to
        // 3 * n, then n is a Triperfect number
        if (sum == 3 * n & n != 1)
            return true;
        else
            return  false;
    }

    // Driver program
    public static void main(String []args)
    {
    int n = 120;

    if (isTriPerfect(n))
        System.out.println(n + " is a Triperfect number");
    }

    //This code is contributed by
    // Ryuga
}

Python3

# Python3 code to check if a given
# number is Triperfect or not

# Returns true if n is Triperfect
def isTriPerfect( n ):

    # To store sum of divisors.
    # Adding 1 and n since they are divisors of n.
    sum = 1 + n

    # Find all divisors and add them
    i = 2
    while i * i <= n:
        if n % i == 0:
            if n / i == i:
                sum = sum + i
            else:
                sum = sum + i + n / i
        i += 1

    # If sum of divisors is equal to
    # 3 * n, then n is a Triperfect number
    return (True if sum == 3 * n and n != 1 else False)

# Driver program
n = 120

if isTriPerfect (n):
    print(n, "is a Triperfect number")

C#

// C# code to check if a given
// number is Triperfect or not
using System;
public class GFG{

    // Returns true if n is Triperfect
    static bool isTriPerfect(int n )
    {
        // To store sum of divisors.
        // Adding 1 and n since they are divisors of n.
        int sum = 1 + n;

        // Find all divisors and add them
        int i = 2;
        while (i * i <= n)
        {
        if (n % i == 0)
            {
                if (n / i == i)
                    sum = sum + i;
                else
                    sum = sum + i + n / i;
            }
            i += 1;
        }

        // If sum of divisors is equal to
        // 3 * n, then n is a Triperfect number
        if (sum == 3 * n & n != 1)
            return true;
        else
            return false;
    }

    // Driver program
    public static void Main()
    {
    int n = 120;

    if (isTriPerfect(n))
        Console.WriteLine(n + " is a Triperfect number");
    }

    //This code is contributed by
    // Mukul Singh
}

PHP

<?PHP
// PHP code to check if a given
// number is Triperfect or not

// Returns true if n is Triperfect
function isTriPerfect($n )
{
    // To store sum of divisors.
    // Adding 1 and n since they
    // are divisors of n.
    $sum = 1 + $n;

    // Find all divisors and add them
    $i = 2;
    while ($i * $i <= $n)
    {
        if ($n % $i == 0)
        {
            if ($n / $i == $i)
                $sum = $sum + $i;
            else
                $sum = $sum + $i + $n / $i;
        }
        $i += 1;
    }

    // If sum of divisors is equal to
    // 3 * n, then n is a Triperfect number
    if ($sum == 3 * $n and $n != 1)
        return true;
    else
        false;
}

// Driver Code
$n = 120;

if (isTriPerfect($n))
    echo $n . " is a Triperfect number";
else
    echo $n . " is not a Triperfect number";

// This code is contributed by mits
?>

Javascript

<script>
    // Javascript code to check if a given
    // number is Triperfect or not

    // Returns true if n is Triperfect
    function isTriPerfect(n)
    {
        // To store sum of divisors.
        // Adding 1 and n since they are divisors of n.
        let sum = 1 + n;

        // Find all divisors and add them
        let i = 2;
        while (i * i <= n)
        {
            if (n % i == 0)
            {
                if (parseInt(n / i, 10) == i)
                    sum = sum + i;
                else
                    sum = sum + i + parseInt(n / i, 10);
            }
            i += 1;
        }

        // If sum of divisors is equal to
        // 3 * n, then n is a Triperfect number
        if (sum == 3 * n & n != 1)
            return true;
        else
            return  false;
    }

    let n = 120;

    if (isTriPerfect(n))
        document.write(n + " is a Triperfect number");

    // This code is contributed by suresh07.
</script>

Output:

120 is a Triperfect number

Time Complexity: O(log n)

Auxiliary Space: O(1)

Some interesting facts about TriPerfect Numbers: 

• Till now only 6 Triperfect numbers are known. These are 120, 672, 523776, 459818240, 1476304896 and 51001180160.
• It has not been proven that more Triperfect Numbers don’t exist but it is believed that these are the only six.

Similarly, we can check for quad-perfect numbers(sum of factors = 4*n), five-perfect numbers( sum of factors = 5*n) and so on. There are currently 36 quad-perfect numbers known and 65 five-perfect numbers known.