In a paper I was reading recently, the author has made use of the following formula in his proof:
Here $\nu(n)$ denotes the number of distinct prime divisors of $n$, $\lambda$ is Liouville's function and $d$ is the divisor function. I don't understand this formula and have not seen it before. Is this true? What would be a proof of it? I feel it must be a simple exercise in number theory, but am unable to prove it at first attempt. Any help will be appreciated. I think the argument for $d$ involves the Jacobi symbol. Is that so? What exactly is this identity?