We define the Liouville function λ(n) by setting λ(1)=1. If n>1, we consider the prime power...

We define the Liouville function λ(n) by setting λ(1)=1. If n>1, we consider the prime power factorization n=p_1^(a_1 ) p_2^(a_2 )…p_m^(a_m ) and define λ(n)=(-1)^(a_1+a_2+⋯+a_m ) Prove that the summatory function of λ,Λ(n)=∑_d|n┤▒〖λ(d)〗 is multiplicative.

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Colby Messinger answered 2 years ago

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