The Möbius function is a mathematical function used in number theory, denoted as μ(n). It assigns values based on the prime factorization of a positive integer n. Specifically, μ(n) equals 1 if n is a product of an even number of distinct prime factors, -1 if n has an odd number of distinct prime factors, and 0 if n has a squared prime factor. This function plays a crucial role in various areas of mathematics, including combinatorics and analytic number theory. It is particularly important in the study of the Möbius inversion formula, which helps in counting and summing functions over integers.