Let n e Z with n > 0. Define an arithmetic function by (1) = 1 and (n) = 2 m

Let n e ∈ Z with n > 0. Define an arithmetic function Ψ by Ψ(1) = 1 and Ψ(n) = 2^m, where m is the number of distinct prime numbers in the prime factorization

of n.

(a) Prove that p is multiplicative but not completely multiplicative.

  

 

(b) Define fin) = din,d>0 if Pa, P2??, Pam is the prime factorization of n, find a formula for p (n) in terms of this prime factorization.