# Math Help - Prove sum of lamda d

1. ## Prove sum of lamda d

Prove that $\sum_{d|n}\lambda(d)= \left\{\begin{array}{ll}1,&\mbox{ if } n=m^2 \mbox{ for some m}\\0,&\mbox{ otherwise } \end{array}\right.$

where $\lambda(n)= (-1)^{\Omega(n)}$ and $\Omega(n)$ is the number of prime divisors of n counting multiplicity.

2. Hint : express the sum as a product taken over the prime powers which divide $n$. (Use the fact that Liouville's function is multiplicative.)