The Möbius inversion formula is a mathematical tool used in number theory and combinatorics. It provides a way to invert summation formulas involving arithmetic functions. Specifically, if you have a function defined by a sum over its divisors, the Möbius inversion allows you to express the original function in terms of the Möbius function, which helps in extracting information about the original function. This formula is particularly useful for solving problems related to counting and partitioning. It connects the sums of functions over divisors with their inverses, enabling mathematicians to derive properties of integers and their relationships through a systematic approach.