Perfect number: A number is called as perfect number when the sum of all it's factors divided by 2 gives the same number as a result. It's very simple, look at below expression 

 (sum of all factors of n)/2 = n
The first positive perfect number is 6. The factors of 6 are 1, 2, 3, and 6. The sum of all the factors of 6 is 12. So, 12/2 gives 6 again.
Algorithm

 BEGIN
  DECLARE sum, i, number
  INITIALIZE sum with 0 and i with 1
  PRINT 'Enter a number'
  ACCEPT number
  LOOP UNTIL I reaches to number
   IF number%i = 0
   THEN
    sum = sum + i
   END IF
  END LOOP
  IF sum/2 = number
  THEN
   PRINT 'Perfect number'
  ELSE
   PRINT 'Not a perfect number'
  END IF
 END
Here is a Java program based on the above algorithm.
PerfectNumber.java

import java.io.*;

/**
 * This class demonstrates the perfect number.
 * @author SANTHOSH REDDY MANDADI
 * @version 1.0
 * @since 27 August 2012
 */

class PerfectNumber
{
  public static void main(String args[]) throws Exception
  {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    System.out.println("Please enter a number:");
    int number = Integer.parseInt(br.readLine());
    if(isPerfectNumber(number))
    {
      System.out.println(number+" is a perfect number.");
    }
    else
    {
      System.out.println(number+" is not a perfect number.");
    }
  }
  public static boolean isPerfectNumber(int number)
  {
    int sum = 0;
    for(int i=1; i<=number; i++)
    {
      if(number%i == 0)
      {
        sum += i;
      }
    }
    if(sum/2 == number)
    {
      return true;
    }
    return false;
  }
}
Output

>java PerfectNumber
Please enter a number:
6
6 is a perfect number.

>java PerfectNumber
Please enter a number:
3
3 is not a perfect number.

>java PerfectNumber
Please enter a number:
8128
8128 is a perfect number.
We can extend the above program to display the list of perfect numbers up to the given number.
PerfectNumbers.java

 import java.io.*;

/**
 * This class prints all perfect numbers upto the given number.
 * @author SANTHOSH REDDY MANDADI
 * @version 1.0
 * @since 27 August 2012
 */
class PerfectNumbers
{
  public static void main(String args[]) throws Exception
  {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    System.out.println("Please enter a number:");
    int number = Integer.parseInt(br.readLine());
    System.out.println("List of perfect numbers between 1 and "+number+": ");
    int count = 0;
    for(int i=2; i<=number;i++)
    {
      if(isPerfectNumber(i))
      {
        System.out.printf("%10d", i);
        count++;
      }
    }
    System.out.println("\n\nThere are "+count+" perfect numbers between 1 and "+number);
  }
  public static boolean isPerfectNumber(int number)
  {
    int sum = 0;
    for(int i=1; i<=number; i++)
    {
      if(number%i == 0)
      {
        sum += i;
      }
    }
    if(sum/2 == number)
    {
      return true;
    }
    return false;
  }
}
Output

>java PerfectNumbers
Please enter a number:
10000
List of perfect numbers between 1 and 10000:
         6        28       496      8128

There are 4 perfect numbers between 1 and 10000

>java PerfectNumbers
Please enter a number:
100000
List of perfect numbers between 1 and 100000:
         6        28       496      8128

There are 4 perfect numbers between 1 and 100000