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LiouvilleLambda

LiouvilleLambda[n]
gives the Liouville function .
  • Integer mathematical function, suitable for both symbolic and numerical manipulation.
Liouville's function gives where is the number of prime factors counting multiplicity:
Plot the sequence:
Liouville's function gives where is the number of prime factors counting multiplicity:
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]=
Evaluate for large arguments:
LiouvilleLambda works over Gaussian integers:
Compute its Dirichlet transform:
LiouvilleLambda threads element-wise over lists:
LiouvilleLambda formatting:
Counting Gaussian integer prime factors:
LiouvilleLambda is completely multiplicative:
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