Are there formulas similar to the Riemann-Weil formula for other arithmetical functions like $ \mu (n) $ or $ \lambda (n) $, for example a sum of the form $ \sum_{n=1}^{\infty}a(n) f(n) $ with this sum being related to the sum over the imaginary part of the Riemann zeros involving the Fourier transform of $ f(x)$?

To summarize: can the Riemann-Weil explicit formulas be generalized to other arithmetical functions? For example:

$$ \sum_{n=1}^{\infty} \frac{\mu(n)}{\sqrt{n}}g(\log n)=\sum_{\gamma}\frac{h( \gamma)}{\zeta '( \rho )}+\sum_{n=1}^{\infty} \frac{1}{\zeta ' (-2n)} \int_{-\infty}^{\infty}dxg(x)e^{-(2n+1/2)x} $$