We have determined the relation between the AGN luminosities at rest-frame 6 {mu}m associated to the dusty torus emission and at 2-10 keV energies using a complete, X-ray flux limited sample of 232 AGN drawn from the Bright Ultra-hard XMM-Newton Survey. The objects have intrinsic X-ray luminosities between 10^42 and 10^46 erg/s and redshifts from 0.05 to 2.8. The rest-frame 6 {mu}m luminosities were computed using data from the Wide-Field Infrared Survey Explorer and are based on a spectral energy distribution decomposition into AGN and galaxy emission. The best-fit relationship for the full sample is consistent with being linear, L_6 {mu}m $propto$ L_2-10 keV^0.99$pm$0.032, with intrinsic scatter, ~0.35 dex in log L_6 {mu}m. The L_6 {mu}m/L_2-10 keV luminosity ratio is largely independent on the line-of-sight X-ray absorption. Assuming a constant X-ray bolometric correction, the fraction of AGN bolometric luminosity reprocessed in the mid-IR decreases weakly, if at all, with the AGN luminosity, a finding at odds with simple receding torus models. Type 2 AGN have redder mid-IR continua at rest-frame wavelengths <12 {mu}m and are overall ~1.3-2 times fainter at 6 {mu}m than type 1 AGN at a given X-ray luminosity. Regardless of whether type 1 and type 2 AGN have the same or different nuclear dusty toroidal structures, our results imply that the AGN emission at rest-frame 6 {mu}m is not isotropic due to self-absorption in the dusty torus, as predicted by AGN torus models. Thus, AGN surveys at rest-frame 6 {mu}m are subject to modest dust obscuration biases.
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