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 prime p and ,
if
and 0 if k > m
I'm given a hint for (c)... Use mathematical induction