Ok, my brain has had time to warm up. What Don points out is not a property of perfect numbers and it's not "one of the "deeper" reasons why these numbers are called "perfect".". If fact, every number with an even number of factors will follow Don's little rule. I pulled 30 out of my hat, but consider its factors:
(1 • 30) = 30
(2 • 15) = 30
(3 • 10) = 30
(5 • 6) = 30
Each of these multiply to the number in question. So, the result of multiplying all the factors must be some multiple of the number being factored
A perfect number can't be a perfect square so it must have an even number of factors. Really Don?
~modest
