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MoebiusMu

MoebiusMu[n]
gives the Möbius function .
MORE INFORMATION
  • 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.
EXAMPLESCLOSE ALL
Basic Examples   (2)
Plot the sequence:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Plot the sequence:
In[1]:=
Click for copyable input
Out[1]=
Scope   (2)
MoebiusMu automatically threads over lists:
Use FullSimplify to simplify MoebiusMu:
Generalizations & Extensions   (2)
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:
Properties & Relations   (4)
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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