// Programmieren 1, Praktikum 3, Aufgabe 3
// Sven Eisenhauer
// 17.11.2004
//
// file: main.cpp
//
// purpose: find "perfect numbers": The sum of all integer factors of a number is the number.          
//          
//
#include <iostream>
using std::cin;
using std::cout;
using std::endl;

int isPerfect(int);

int main()
{
	// how far to search
	const int maxNumbers=1000;

	for (int j=1;j<=maxNumbers;j++)
	{
		if (0 == isPerfect(j))
		{
			cout << ": " << j << endl;
		}
	}

	cout << "\n";

	return 0;
}

int isPerfect(int number)
{
    int sum=0;
    // check for all numbers between the number, exclusive the number itself and 1 inclusive
	for (int i=number-1;i>=1;i--)
	{
		// is the actual number a factor???
		if (0 == number%i)
		// if it is, add it
			sum+=i;
	}
	// the sum of all factors... and so on
	if (sum == number)
	{
		// so we have a perfect number here... fine... find the factors again and cout them
		for (int k=number-1;k>=1;k--)
			if (0 == number%k)
				cout << k << " ";
		return 0;
	}
	else
		return 1;
}