Super-Poulet Number

Super-Poulet number is a Poulet number (pseudoprime) to base 2 if each and every divisor D divides .

Some of the super-poulet numbers are: 

341, 1387, 2047, 2701, 3277, 4033…. 

Check if N is a Super-poulet number

Given an integer N, the task is to check N is a Super-Poulet Number.

Examples:

Input: N = 341 
Output: Yes
Input: N = 10 
Output: No 

Approach: The idea is to generate all the divisors of the number N and for all divisor check D divides . If this condition satisfy for all divisors then the number is super-poulet number.
For Example:

For N = 341,
Divisors of 341 are {1, 11, 31, 341} and, 



Similarly, also gives integer value. 
Therefore, 341 is a super-poulet number. 

Below is the implementation of the above approach:

C++

// C++ implementation to
// check if N is a super Poulet number
#include <bits/stdc++.h>

using namespace std;

// Function to find the divisors
vector<int> findDivisors(int n)
{
  vector<int> divisors;

  // Loop to iterate over the
  // square root of the N
  for (int i = 1; i < (sqrt(n) + 1); i++) {
    if (n % i == 0) {

      // Check if divisors are equal
      if (n / i == i)
        divisors.push_back(i);
      else {
        divisors.push_back(i);
        divisors.push_back((n / i));
      }
    }
  }
  sort(divisors.begin(), divisors.end());
  return divisors;
}

// Function to check if N
// is a super Poulet number
bool isSuperdNum(int n)
{
  vector<int> d = findDivisors(n);

  // Loop to check that every
  // divisor divides 2^D - 2
  for (int i : d) {
    double x = (pow(2, i) - 2) / i;
    if (floor(x) != x)
      return false;
  }
  return true;
}

// Driver Code
int main()
{
  int n = 341;
  if (isSuperdNum(n) == true)
    cout << "Yes";
  else
    cout << "No";
}

// This code is contributed by phasing17.

Java

// Java implementation to
// check if N is a super Poulet number
import java.util.*;

class GFG
{

  // Function to find the divisors
  static ArrayList<Integer> findDivisors(int n)
  {
     ArrayList<Integer> divisors = new  ArrayList<Integer>();

    // Loop to iterate over the
    // square root of the N
    for (int i = 1; i < (Math.sqrt(n) + 1); i++)
    {
      if (n % i == 0)
      {

        // Check if divisors are equal
        if (n / i == i)
          divisors.add(i);
        else
        {
          divisors.add(i);
          divisors.add((n / i));
        }
      }
    }
    Collections.sort(divisors);
    return divisors;
  }

  // Function to check if N
  // is a super Poulet number
  static boolean isSuperdNum(int n)
  {
     ArrayList<Integer> d = findDivisors(n);

    // Loop to check that every
    // divisor divides 2^D - 2
    for(int i : d)
    {
      double x = (Math.pow(2, i) - 2) / i;
      if (Math.floor(x) != x)
        return false;
    }
    return true;
  }

  // Driver Code
  public static void main(String[] args)
  {
    int n = 341;
    if (isSuperdNum(n) == true)
      System.out.print("Yes");
    else
      System.out.print("No");
  }
}

// This code is contributed by phasing17.

Python3

# Python3 implementation to
# check if N is a super Poulet number
import math

# Function to find the divisors
def findDivisors(n):
    divisors = []

    # Loop to iterate over the
    # square root of the N
    for i in range(1,\
         int(math.sqrt(n) + 1)):

        if (n % i == 0) :

            # Check if divisors are equal
            if (n / i == i):
                divisors.append(i)
            else:
                divisors.append(i)
                divisors.append(int(n / i))
    return sorted(divisors)

# Function to check if N
# is a super Poulet number
def isSuperdNum(n):
    d = findDivisors(n)

    # Loop to check that every
    # divisor divides 2^D - 2
    for i in d:
        x = (2**i-2)/i
        if int(x) != x:
            return False
    return True

# Driver Code
if __name__ == "__main__":
    n = 341
    if isSuperdNum(n) == True:
        print("Yes")
    else :
        print("No")

C#

// C# implementation to
// check if N is a super Poulet number
using System;
using System.Collections.Generic;

class GFG
{

  // Function to find the divisors
  static List<int> findDivisors(int n)
  {
    List<int> divisors = new List<int>();

    // Loop to iterate over the
    // square root of the N
    for (int i = 1; i < (Math.Sqrt(n) + 1); i++)
    {
      if (n % i == 0)
      {

        // Check if divisors are equal
        if (n / i == i)
          divisors.Add(i);
        else
        {
          divisors.Add(i);
          divisors.Add((n / i));
        }
      }
    }
    divisors.Sort();
    return divisors;
  }

  // Function to check if N
  // is a super Poulet number
  static bool isSuperdNum(int n)
  {
    List<int> d = findDivisors(n);

    // Loop to check that every
    // divisor divides 2^D - 2
    foreach(int i in d)
    {
      double x = (Math.Pow(2, i) - 2) / i;
      if (Math.Truncate(x) != x)
        return false;
    }
    return true;
  }

  // Driver Code
  public static void Main(string[] args)
  {
    int n = 341;
    if (isSuperdNum(n) == true)
      Console.Write("Yes");
    else
      Console.Write("No");
  }
}

// This code is contributed by chitranayal.

Javascript

<script>
// Javascript implementation to
// check if N is a super Poulet number

// Function to find the divisors
function findDivisors(n){
    let divisors = []

    // Loop to iterate over the
    // square root of the N
    for(let i = 1; i < Math.floor(Math.sqrt(n) + 1); i++){

        if (n % i == 0) {

            // Check if divisors are equal
            if (n / i == i){
                divisors.push(i)
            }
            else{
                divisors.push(i)
                divisors.push(Math.floor(n / i))
            }
        }
    }
    return divisors.sort((a, b)=> a - b)
}

// Function to check if N
// is a super Poulet number
function isSuperdNum(n){
    let d = findDivisors(n)

    // Loop to check that every
    // divisor divides 2^D - 2
    for(let i in d){
        let x = (2**i - 2) / i

        if (Math.floor(x) != x){
            return false
        }
    }
    return true
}
// Driver Code
    let n = 341
    if(isSuperdNum(n) == true){
        document.write("Yes")
    }
    else {
        document.write("No")
    }

// This code is contributed by _saurabh_jaiswal

</script>

Output:

Yes