Möbius function

The Möbius function is a mathematical tool used in number theory to analyze the structure of numbers, especially regarding their factors. For a positive integer n, it assigns a value: 0 if n has a squared prime factor (like 4, which is 2 squared), +1 if n is a product of an even number of distinct primes, and -1 if it’s a product of an odd number of distinct primes. This function helps in counting and understanding the distribution of prime factors, playing a key role in the Möbius inversion formula, which uncovers relationships between arithmetic functions.