We present a systematic X-ray study, the third in a series, of 49 active galactic nuclei with intermediate-mass black holes (IMBH; ~10^5-10^6 M_sun) using Chandra observations. We detect 42 out of 49 targets with a 0.5-2 keV X-ray luminosity 10^41-10^43 erg/s. We perform spectral fitting for the 10 objects with enough counts (>200), and they are all well fit by a simple power-law model modified by Galactic absorption, with no sign of significant intrinsic absorption. While we cannot fit the X-ray spectral slope directly for the rest of the sample, we estimate it from the hardness ratio and find a range of photon indices consistent with those seen in more luminous and massive objects. The X-ray-to-optical spectral slope (alphaox) of our IMBH sample is systematically flatter than in active galaxies with more massive black holes, consistent with the well-known correlation between alphaox and UV luminosity. Thanks to the wide dynamic range of our sample, we find evidence that alphaox increases with decreasing M_BH as expected from accretion disk models, where the UV emission systematically decreases as M_BH decreases and the disk temperature increases. We also find a long tail toward low alphaox values. While some of these sources may be obscured, given the high L_bol/L_Eddington values in the sample, we argue that some may be intrinsically X-ray-weak, perhaps owing to a rare state that radiates very little coronal emission.
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