Liouville function

The Liouville function is defined by $\lambda(1)=1$ and $\lambda(n)=(-1)^{k_{1}+k_{2}+\cdots+k_{r}}$ , if the prime factorization of $n>1$ is $n=p_{1}^{k_{1}}p_{2}^{k_{2}}\cdots p_{r}^{k_{r}}$ (where each $p_{i}$ is positive). This function is completely multiplicative and the

\sum_{d|n}\lambda(d)=\begin{cases}1&\text{if $n=m^{2}$ for some integer $m$}\\ 0&\text{otherwise,}\end{cases}

where the sum runs over all positive divisors of $n$ .