One identity about Eisenstein series and L functions of modular forms

Question

Currently, I'm reading Zagier's notes 'Modular forms whose Fourier coefficients involve zeta-function of quadratic fields'. There is an equation (72) in page 42: $$\sum_{n=1}^{\infty} \frac{\sigma_{r}(n) a(n)}{n^s}=\frac{L_{f}(s) L_{f}(s-r)}{\zeta(2 s-r-k+1)} \quad\left(\operatorname{Re}(s)>r+\frac{k+1}{2}\right).$$ But I don't how to prove it and also didn't find its proof in the note. How can we prove it? Are there some references and suggestions? Thank you very much!