The function "ψ(n)", known as the psi function, is a mathematical function that counts the number of prime factors of a positive integer n, counting multiplicities. For example, if n is 18, which has the prime factorization of 2 × 3², then ψ(18) equals 3, since there are three prime factors (one 2 and two 3s). The psi function is closely related to other number-theoretic functions, such as the Euler's totient function and the Mertens function. It is often used in analytic number theory to study the distribution of prime numbers and their properties within integers.