Giant X-ray outbursts, with luminosities of about $ 10^{37}$ erg s$^{-1}$, are observed roughly every 5 years from the nearby Be/pulsar binary 1A 0535+262. In this article, we present observations of the source with VERITAS at very-high energies (VHE; E$>$100 GeV) triggered by the X-ray outburst in December 2009. The observations started shortly after the onset of the outburst, and they provided comprehensive coverage of the episode, as well as the 111-day binary orbit. No VHE emission is evident at any time. We also examined data from the contemporaneous observations of 1A 0535+262 with the Fermi/LAT at high energy photons (HE; E$>$0.1 GeV) and failed to detect the source at GeV energies. The X-ray continua measured with the Swift/XRT and the RXTE/PCA can be well described by the combination of blackbody and Comptonized emission from thermal electrons. Therefore, the gamma-ray and X-ray observations suggest the absence of a significant population of non-thermal particles in the system. This distinguishes 1A~0535+262 from those Be X-ray binaries (such as PSR B1259--63 and LS I +61$^{circ}$303) that have been detected at GeV--TeV energies. We discuss the implications of the results on theoretical models.
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