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 $n$ .

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