MoebiusMu[n] gives the Möbius function .
Integer mathematical function (see Section A.3.10).
is if is a product of an even number of distinct primes, if it is a product of an odd number of primes, and if it has a multiple prime factor.
See The Mathematica Book: Section 3.2.4.
See also: Divisors, FactorInteger, JacobiSymbol.