An important population of the dayside Martian ionosphere are photoelectrons that are produced by solar Extreme Ultraviolet and X-ray ionization of atmospheric neutrals. A typical photoelectron energy spectrum is characterized by a distinctive peak near 27 eV related to the strong solar HeII emission line at 30.4 nm, and an additional peak near 500 eV related to O Auger ionization. In this study, the extensive measurements made by the Solar Wind Electron Analyzer on board the recent Mars Atmosphere and Volatile Evolution spacecraft are analyzed and found to verify the scenario that Martian ionosphere photoelectrons are driven by solar radiation. We report that the photoelectron intensities at the centers of both peaks increase steadily with increasing solar ionizing flux below 90 nm and that the observed solar cycle variation is substantially more prominent near the O Auger peak than near the HeII peak. The latter observation is clearly driven by a larger variability in solar irradiance at shorter wavelengths. When the solar ionizing flux increases from 1 mW·m-2 to 2.5 mW·m-2, the photoelectron intensity increases by a factor of 3.2 at the HeII peak and by a much larger factor of 10.5 at the O Auger peak, both within the optically thin regions of the Martian atmosphere.