\lambda(n) = (-1)^{a1+a2+....+ak} where n = \prod pi^{ai} for distinct primes pi
g(n) = 1 if n = 1 or n = \prod pi for distinct primes pi
and g(n) = 0 otherwise

Assume \lambda and g are multiplicative.

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

b) Let \Lambda = (\lambda * po) be the summatory function of \lambda. Prove that
\Lambda(n) = 1 if n is a perfect square and 0 otherwise

c) Define a collection of arithmetic functions g^{(m)} : Z^+ \rightarrow \complex as follows:
g^{(1)} = g
g^{(m)} = (g * g^{(m-1)}) for m \geq 2
Prove that g^{(m)} is multiplicative for all m \in Z^+ and show that for any prime p and k \in Z^+,
g^{(m)}(p^k) = \left(\begin{array}{cc}m\\k\end{array}\right) if 0 \leq k \leq m
and 0 if k > m

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