Números perfeitos e amigáveis - Santos Júnior, Raimundo João dos (2020)
The perfect numbers, as well as the friendly numbers, began to be studied by the pythagorean school and up to the current days they wake the curiosity of many theoreticians of the numbers. In spite of being relatively simple topics, in the sense of finding elementary concepts, like dividing and function σ(n) a sum of divisors, there are still some problems when in it was opened inherent, and this has been causing more and more scholars to develop more substantial techniques in order to find a satisfactory solution for each of these problems. In this work, we consider some relative properties to these numbers, boarding, in a special form, the central theorem that characterizes the perfect equal numbers, a narrow relation of these numbers with the cousins of Mersenne. We consider, also, some problems that are classics of the subject with its respective solutions.