Prove that for every positive integer n, we have

Sum[for all m|n](μ(m)*σ(n/m)) = n.

Here, μ(x) is the mobius function and σ(x) is the sum of all positive divisors of x.

I'm not sure where to begin with this. Since μ and σ are multiplicative, I think I could get

Sum[for all m|n](μ(m)*σ(n/m)) = Sum[for all m|n](μ(n/m)*σ(m))

but I don't know how useful that is.