//	Check weather a number is  a perfect number
//	Variant 1: Brute force
//		g++ -Wno-deprecated PerfectNum1.cc 

#include <iostream.h>
#include <math.h>

main()
{
 long long int a,		// number to investigate
 	       i,n,		// loop index and last index
	       sum_a;		// sum of all factors

 cout << endl << "  Input  a = ";
 cin  >> a;
 cout << endl;
 
 n = a/2;			// potentially largest factor
 
 sum_a = 0;
 for ( i=1; i<=n; i++ )
  {
    if ( ( a % i ) == 0 )	// is var.  i  a factor?
     {
       sum_a += i;
     }
  }

 cout << " a =  " << a << "   is ";
 if ( sum_a != a)		// sum of factors not equal number  a ?
  {
    cout << "not ";
  }
 cout << "a perfect number" << endl << endl;
 
}








/*
Perfect numbers are:
6

28

496

8128

33550336		// Laptop: user    0m0.545 / 0m1.736s  fuer 4/8 Byte-int

8589869056		// Here, we need 8 Byte integers (long long int)
			// Laptop: user    7m25.344s


*/