Integer part of the geometric mean of the divisors of N

Given an integer N, the task is to find the integer part of the geometric mean of the divisors of N. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers), and so on.

Examples:
Input: N = 4 
Output: 2 
Divisors of 4 are 1, 2 and 4 
Geometric mean = (1 * 2 * 4)^(1/3) = 8^(1/3) = 2
Input: N = 16 
Output: 8 
Divisors of 16 are 1, 2, 4, 8 and 16 
Geometric mean = (1 * 2 * 4 * 8 * 16)^(1/5) = 1024^(1/5) = 4 

Approach: It can be observed that a series will be formed for the values of N as 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, ….. whose N^th term is ??n?.
Below is the implementation of the above approach: 

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to return the integer
// part of the geometric mean
// of the divisors of n
int geometricMean(int n)
{
    return sqrt(n);
}

// Driver code
int main()
{
    int n = 16;

    cout << geometricMean(n);

    return 0;
}

Java

// Java implementation of the approach
class GFG
{

// Function to return the integer
// part of the geometric mean
// of the divisors of n
static int geometricMean(int n)
{
    return (int) Math.sqrt(n);
}

// Driver code
public static void main(String []args)
{
    int n = 16;
    System.out.println(geometricMean(n));
}
}

// This code is contributed by Rajput-Ji

Python3

# Python3 implementation of the approach
from math import sqrt

# Function to return the integer
# part of the geometric mean
# of the divisors of n
def geometricMean(n) :

    return int(sqrt(n));

# Driver code
if __name__ == "__main__" :

    n = 16;

    print(geometricMean(n));

# This code is contributed by AnkitRai01

C#

// C# implementation of the approach
using System;

class GFG
{

// Function to return the integer
// part of the geometric mean
// of the divisors of n
static int geometricMean(int n)
{
    return (int) Math.Sqrt(n);
}

// Driver code
public static void Main(String []args)
{
    int n = 16;
    Console.WriteLine(geometricMean(n));
}
}

// This code is contributed by PrinciRaj1992

Javascript

<script>

// Javascript implementation of the approach

// Function to return the integer
// part of the geometric mean
// of the divisors of n
function geometricMean(n)
{
    return Math.sqrt(n);
}

// Driver code
var n = 16;
document.write(geometricMean(n));

</script>

Output:

4

Time Complexity: O(logn) because using inbuilt sqrt function

Auxiliary Space: O(1)