Möbius Function

The Möbius function, written mu(n), is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius in 1832. It is ubiquitous in elementary and analytic number theory and most often appears through its namesake, the Möbius inversion formula; following work by Gian-Carlo Rota in the 1960s, generalized versions of the function were also introduced into combinatorics. The function is defined to equal one when n equals one, to equal negative one raised to the power k when n is a product of k distinct prime numbers, and to equal zero whenever n is divisible by a perfect square greater than one.