electrodynamics with a funky coupling

Imagine, the Maxwell-action was given by \(S = \int\mathrm{d}^4x\:R_{\alpha\beta\mu\nu}F^{\alpha\mu}F^{\beta\nu}\) with the Riemann-curvature \(R_{\alpha\beta\mu\nu}\) and the Faraday-tensor \(F^{\alpha\mu}\). Would this be a viable action? What would be the corresponding field equations for the Maxwell field \(A^\mu\)?