New properties of divisors of natural number

The divisors of a natural number are very important for several areas of mathematics, representing a promising field in number theory. This work sought to analyze new relations involving the divisors of natural numbers, extending them to prime numbers. These are relations that may have an interesting application for counting the number of divisors of any natural number and understanding the behavior of prime numbers. They are not a primality test, but they can be a possible tool for this and could also be useful for understanding the Riemann's zeta function that is strongly linked to the distribution of prime numbers.