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 cane 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 Nth term is ⌊√n⌋.

Below is the implementation of the above approach:

C++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

4


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