where for distinct primes pi

g(n) = 1 if n = 1 or n = for distinct primes pi

and g(n) = 0 otherwise

Assume and g are multiplicative.

a) Prove that g is the inverse of under the Dirichlet convolution operation.

b) Let be the summatory function of . Prove that

if n is a perfect square and 0 otherwise

c) Define a collection of arithmetic functions as follows:

for

Prove that is multiplicative for all and show that for any primepand ,

if

and 0 if k > m

I'm given a hint for (c)...Use mathematical induction