This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# MoebiusMu

 MoebiusMu[n]gives the Möbius function .
• Integer mathematical function, suitable for both symbolic and numerical manipulation.
• is if n 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.
Plot the sequence:
 Out[1]=
 Out[2]=

Plot the sequence:
 Out[1]=
 Scope   (2)
Use FullSimplify to simplify MoebiusMu:
MoebiusMu works for negative integers:
MoebiusMu works for Gaussian integers:
 Applications   (2)
The :
Plot of Sqrt[n]-m[n]:
Dirichlet generating function of MoebiusMu:
Compare with DirichletTransform:
The number is square free and factors into an odd number of distinct primes:
Here is square free and factors into an even number of distinct primes:
The number is not square free:
MoebiusMu is multiplicative for coprime elements:
EulerPhi can be expressed in terms of MoebiusMu:
MoebiusMu is related to DivisorSigma through the Möbius inversion formulas:
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