Classifications of Perfect Numbers

Have you ever heard the expression "No one is perfect?" Well, technically speaking, "1" is not a perfect number (though this is probably not where the expression comes from). Have you ever stopped to think, "What is a perfect number?" Come explore the world of perfect, quasi-perfect, pseudoperfect, weird, multiperfect, and hyperperfect numbers with us. We will briefly discuss some of these classifications and the number theoretical problems associated with them.

Some of the problems we will study have been unproven for thousands (yes, thousands) of years. We will discuss sections of Richard Guy's book, Unsolved Problems in Number Theory, to get an idea of what progress has been made toward solutions to classical questions like, "Are there any odd Perfect Numbers?" Moreover, we will study significant conjectures and results for some the classifications of perfect numbers listed above. Our research will include sections of current papers such as Some New Results On Even Almost Perfect Numbers Which Are Not Powers Of Two and On The Representation Of An Even Perfect Number As The Sum Of A Limited Number Of Cubes.