‘Perfect and not so perfect numbers’ examines the concept of perfect numbers. Perfect numbers are numbers which are the sum of their proper factors. Euclid showed that perfect numbers had a relationship with a special type of prime called a Mersenne number. Euler expanded on this to give a direct relationship between Mersenne numbers and perfect numbers. Amicable pairs are pairs of numbers whose proper factors sum to each other. A number's aliquot sequence can be found by repeatedly summing a number's factors to get a new number. Numbers can be deficient, perfect, or abundant, depending on the sum of their factors.