Number of elements with even factors in the given range

Given a range [n, m], the task is to find the number of elements that have even number of factors in the given range (n and m inclusive).

Examples :

Input: n = 5, m = 20
Output: 14
The numbers with even factors are 
5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20.

Input: n = 5, m = 100
Output: 88


A Simple Solution is to loop through all numbers starting from n. For every number, check if it has an even number of factors. If it has an even number of factors then increment count of such numbers and finally print the number of such elements. To find all divisors of a natural number efficiently, refer All divisors of a natural number

An Efficient Solution is to find the numbers with odd number of factors i.e only the perfect squares have odd number of factors, so all numbers other than perfect squares will have even number of factors. So, find the count of perfect squares in the range and subtract from the total numbers i.e. m-n+1 .

Below is the implementation of the above approach:

C++

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// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to count the perfect squares
int countOddSquares(int n, int m)
{
    return (int)pow(m, 0.5) - (int)pow(n - 1, 0.5);
}
  
// Driver code
int main()
{
    int n = 5, m = 100;
    cout << "Count is "
         << (m - n + 1) - countOddSquares(n, m);
    return 0;
}

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Java

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// Java implementation of the above approach
import java.io.*;
  
class GFG 
{
      
// Function to count the perfect squares
static int countOddSquares(int n, int m)
{
    return (int)Math.pow(m, 0.5) -
            (int)Math.pow(n - 1, 0.5);
}
  
// Driver code
public static void main (String[] args)
{
    int n = 5, m = 100;
    System.out.println("Count is " + ((m - n + 1)
                    - countOddSquares(n, m)));
}
}
  
// This code is contributed by ajit..

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Python 3

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# Python3 implementation of the
# above approach 
  
# Function to count the perfect squares 
def countOddSquares(n, m) : 
    return (int(pow(m, 0.5)) - 
            int(pow(n - 1, 0.5))) 
  
# Driver code 
if __name__ == "__main__" :
  
    n = 5 ; m = 100
    print("Count is", (m - n + 1) - 
                       countOddSquares(n, m)) 
      
# This code is contributed by Ryuga

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C#

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// C# implementation of the above approach
using System;
  
class GFG
{
          
// Function to count the perfect squares
static int countOddSquares(int n, int m)
{
    return (int)Math.Pow(m, 0.5) -
            (int)Math.Pow(n - 1, 0.5);
}
  
// Driver code
static public void Main ()
{
    int n = 5, m = 100;
    Console.WriteLine("Count is " + ((m - n + 1)
                    - countOddSquares(n, m)));
}
}
  
// This Code is contributed by akt_mit.

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PHP

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<?php
// PHP implementation of the 
// above approach
  
// Function to count the perfect squares
function countOddSquares($n, $m)
{
    return (int)pow($m, 0.5) - 
           (int)pow($n - 1, 0.5);
}
  
// Driver code
$n = 5;
$m = 100;
echo "Count is ", ($m - $n + 1) -
                   countOddSquares($n, $m);
      
// This code is contributed by ajit
?>

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Output:

Count is 88


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Improved By : jit_t, AnkitRai01