Write a method called perfectNumbers that accepts an integer maximum as its parameter and prints all "perfect numbers" up to and including that maximum. A perfect number is an integer that is equal to the sum of its proper factors, that is, all numbers that evenly divide it other than itself. For example, 28 is a perfect number because 1 + 2 + 4 + 7 + 14 = 28. The call perfectNumbers(500); should produce the following output:

Perfect numbers up to 500: 6 28 496 

Your program should be called FindPerfectNumbers.java

If a negative number is given to perfectNumbers, an IllegalArgumentException should be thrown.

HINT: Break the problem up into smaller sub-problems.

Write code to determine whether a given integer is a perfect number.

Write code to find all perfect numbers in a given range using the code you wrote in the first sub-problem.