SOLVING SOME SPECIAL TASKS FOR ARITHMETIC FUNCTIONS AND PERFECT NUMBERS

摘要

Arithmetic functions help us determine which of the three sets (abundant, deficient, perfect) a given number belongs to. Arithmetic functions can also be used to identify various other properties of numbers and they have a special position in the number theory. This paper points to the fact that arithmetic functions can be used to solve various special practical tasks and determine the properties of numbers. The paper also highlights the relationship between Mersenne numbers and perfect numbers, as well as the issues connected with the search for the highest primes.