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
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more succinctly expressed as
One unique fact about the Mobius function, which leads to the Mobius inversion formula, is that