The Rho function, denoted as ρ(n), is a mathematical function that counts the number of distinct prime factors of a positive integer n. It is particularly useful in number theory, where understanding the prime factorization of numbers is essential for various applications, including cryptography and algorithm design. In addition to its basic definition, the Rho function can also be related to other functions, such as the Euler's totient function and the Möbius function. These relationships help mathematicians analyze the properties of integers and their prime factors more deeply, contributing to the broader field of analytic number theory.