##  [Liouville Function](/liouville-function) 

  ##  [Liouville Function](https://puremath.quantumdictionary.io/liouville-function-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Completely multiplicative arithmetic function λ(n)=(-1)^{Ω(n)}, where Ω(n) is the total number of prime factors of n counted with multiplicity; takes values ±1 and extends multiplicativity to prime powers by λ(p^k)=(-1)^k.