Mobius function
The Mobius function is a multiplicative number theoretic function defined as follows: In addition, .
The Mobius function is useful for a variety of reasons.
First, it conveniently encodes Principle of Inclusion-Exclusion. For example, to count the number of positive integers less than or equal to and relatively prime to , we have
more succinctly expressed as
One unique fact about the Mobius function, which leads to the Mobius inversion formula, is that
The Mobius function is also closely related to the Riemann zeta function, as