# Count integers in a range which are divisible by their euler totient value

Given 2 integers L and R, the task is to find out the number of integers in the range [L, R] such that they are completely divisible by their Euler totient value.

Examples:

Input: L = 2, R = 3
Output: 1 (2) = 2 => 2 % (2) = 0 (3) = 2 => 3 % (3) = 1
Hence 2 satisfies the condition.

Input: L = 12, R = 21
Output: 3
Only 12, 16 and 18 satisfy the condition.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: We know that the euler totient function of a number is given as follows: Rearranging the terms, we get: If we take a close look at the RHS, we observe that only 2 and 3 are the primes that satisfy n % = 0. This is because for primes p1 = 2 and p2 = 3, p1 – 1 = 1 and p2 – 1 = 2. Hence, only numbers of the form 2p3q where p >= 1 and q >= 0 need to be counted while lying in the range [L, R].

Below is the implementation of the above approach:

## C++

 // C++ implementation of the above approach.  #include     #define ll long long  using namespace std;     // Function to return a^n  ll power(ll a, ll n)  {      if (n == 0)          return 1;         ll p = power(a, n / 2);      p = p * p;         if (n & 1)          p = p * a;         return p;  }     // Function to return count of integers  // that satisfy n % phi(n) = 0  int countIntegers(ll l, ll r)  {         ll ans = 0, i = 1;      ll v = power(2, i);         while (v <= r) {             while (v <= r) {                 if (v >= l)                  ans++;              v = v * 3;          }             i++;          v = power(2, i);      }         if (l == 1)          ans++;         return ans;  }     // Driver Code  int main()  {      ll l = 12, r = 21;      cout << countIntegers(l, r);         return 0;  }

## Java

 // Java implementation of the above approach.  class GFG   {     // Function to return a^n  static long power(long a, long n)  {      if (n == 0)          return 1;         long p = power(a, n / 2);      p = p * p;         if (n%2== 1)          p = p * a;         return p;  }     // Function to return count of integers  // that satisfy n % phi(n) = 0  static int countIntegers(long l, long r)  {         long ans = 0, i = 1;      long v = power(2, i);         while (v <= r)       {          while (v <= r)           {                 if (v >= l)                  ans++;              v = v * 3;          }             i++;          v = power(2, i);      }         if (l == 1)          ans++;         return (int) ans;  }     // Driver Code  public static void main(String[] args)  {      long l = 12, r = 21;      System.out.println(countIntegers(l, r));  }  }     // This code contributed by Rajput-Ji

## Python3

 # Python3 implementation of the approach      # Function to return a^n   def power(a, n):          if n == 0:           return 1        p = power(a, n // 2)       p = p * p          if n & 1:           p = p * a          return p      # Function to return count of integers   # that satisfy n % phi(n) = 0   def countIntegers(l, r):          ans, i = 0, 1     v = power(2, i)          while v <= r:              while v <= r:                  if v >= l:                   ans += 1                            v = v * 3            i += 1         v = power(2, i)              if l == 1:           ans += 1        return ans      # Driver Code   if __name__ == "__main__":         l, r = 12, 21     print(countIntegers(l, r))          # This code is contributed   # by Rituraj Jain

## C#

 // C# implementation of the above approach.  using System;     class GFG   {     // Function to return a^n  static long power(long a, long n)  {      if (n == 0)          return 1;         long p = power(a, n / 2);      p = p * p;         if (n % 2 == 1)          p = p * a;         return p;  }     // Function to return count of integers  // that satisfy n % phi(n) = 0  static int countIntegers(long l, long r)  {         long ans = 0, i = 1;      long v = power(2, i);         while (v <= r)       {          while (v <= r)           {                 if (v >= l)                  ans++;              v = v * 3;          }             i++;          v = power(2, i);      }         if (l == 1)          ans++;         return (int) ans;  }     // Driver Code  public static void Main()  {      long l = 12, r = 21;      Console.WriteLine(countIntegers(l, r));  }  }     /* This code contributed by PrinciRaj1992 */

## PHP

 = $l)   $ans++;               $v = $v * 3;           }              $i++;   $v = power(2, $i);   }     if ($l == 1)           $ans++;     return $ans;   }      // Driver Code   $l = 12;  $r = 21;      echo countIntegers($l, $r);      // This code is contributed by Ryuga  ?>

Output:

3


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