/***************************************************
Student Name:      Samantha Eaton
Prof/section:      Bielajew/300
GSI section:       cat/306
File:              hwk5b.cpp
Purpose:           To find the "perfect" numbers
***************************************************/

#include <iostream>
#include <cmath>

using namespace std;

//function that finds the prime number.
bool perfectNumber(int A)
{   int c = 0, N = 0, B;

   //uses equation to find prime number.
   B = static_cast<int>(pow((float)2,(float)A) -1.0);

    bool isPrime, isPerfect=0;

      for (int i = 2; i < B; i = i + 1)
      {
          if (B%i == 0)
          {
             isPrime = 1;
             c = c + 1;
          }
       }

    //else is prime
    if (c == 0)
    {
       isPrime = 0;
    }

//Perfect number.
   if (isPrime == 1)
   {
      N= static_cast<int>( pow((float)2,(float)(A - 1.0)) )*
	 static_cast<int>(( pow((float)2,(float)A) - 1.0) );

      //even number.
      if (N%2 == 0)
      {
         isPerfect = 1;
      }
   }
return isPerfect;
}


void printPerfect(int N)
{
   cout << N << " is a perfect number" << endl;
   cout << N << " = " << "1";

   //Finds divisable numbers.
   for (int i = 2; i < N; i = i + 1)
   {
      if (N%i == 0)
      {
         cout << " + " << i;
      }
   }
   cout << endl;

return;
}
/***************************************************
Purpose: Find the first 5 perfect numbers
Recieves: nothing
Returns: outputs perfect numbers and what they are made of
****************************************************/
int main(void)
{
bool Perfect;
int N = 0, count = 5, A = 1;
while (count <= 1)
{
   Perfect = perfectNumber(A);
   if (Perfect==1)
   {
      N= static_cast<int>( pow((double)2,((double)A - 1.0)) )*
	 static_cast<int>( ( pow((double)2,(double)A) - 1.0) );
      count = count + 1;
      printPerfect(N);
   }
   A = A + 1;
}

   return 0;
}