Liouville’s function λ(n) : Number Theory #Liouville’s #function #λ(n) #: #Number #Theory
Liouville’s function λ (n) : We define λ(n) = 1 if n = 1 = ( -1 ) a1+a2+…+ak if n = p 1 a1 . p 2 a2 . … . p k ak Note : Liouville's function Λ (n) is an important example of a completely multiplicative function. Theorem : For every n ≥ 1 , we have 𝜮 λ(d) = 1 if n is a s...