//	Find perfect numbers.
//	derived from Variant 2:  i  is  a factor of  <=>  a/i  is a factor of a
//		g++ -Wno-deprecated PerfectNum3.cc 

#include <iostream.h>
#include <math.h>
#include <limits.h>		// max ULL-int number: ULLONG_MAX

main()
{
 const unsigned long long int   // interval to investigate
 			iv1 = 1ULL,		// 1
//			iv1 = 8589869000,	// max. number
			iv2 = 300000;	// max. number
//			iv2 = 8589869100;	// max. number
// 			iv2 = ULONG_LONG_MAX;	// max. number
// 			iv2 = ULLONG_MAX;	// undefined in g++
 const unsigned long long int
 		i_chk = iv2/1000;// check progress of work after i_chek loops
 unsigned long long int a,	// number to investigate
 	       	        i,n,	// loop index and last index
	                sum_a;	// sum of all factors


 cout << endl << "  Start finding of perfect numbers " << endl << endl;

 for ( a=iv1; a<=iv2; a++ )
  {
      if ( a%i_chk == 0) 		// Check the progress of the work
      { 
        cout << "."; 
      }
//	-----------  code from Var. 2  [start]  ------------------------
     n = floor(sqrt(a));	// NEW: last potential factor in Var.2

     sum_a = 1;			// NEW: Don't forget 1
     for ( i=2; i<=n; i++ )		// NEW: we will start with 2
      {
	if ( ( a % i ) == 0 )	// is var.  i  a factor?
	 {
	   sum_a += i + a/i;	// NEW: add also  a/i
	 }
      }
//	-----------  code from Var. 2  [end]  --------------------------

     if ( sum_a == a)		// output if var.  a  is a perfect number 
      {
	cout << endl << " Perfect number: " << a  << endl;
      }
  }
 
 cout << endl;
}








/*
Perfect numbers are:
6

28

496

8128

33550336		// Laptop: user    0m0.002 / 0m0.004s  fuer 4/8 Byte-int

8589869056		// Here, we need 8 Byte integers (long long int)
			// Laptop: user    0m0.013s  [old: 7m25.344s]


*/