  Spectra of positively charged kaons in p+C interactions at 31 GeV/c were
measured with the NA61/SHINE spectrometer at the CERN SPS. The analysis is
based on the full set of data collected in 2007 with a graphite target with a
thickness of 4% of a nuclear interaction length. Interaction cross sections and
charged pion spectra were already measured using the same set of data. These
new measurements in combination with the published ones are required to improve
predictions of the neutrino flux for the T2K long baseline neutrino oscillation
experiment in Japan. In particular, the knowledge of kaon production is crucial
for precisely predicting the intrinsic electron neutrino component and the high
energy tail of the T2K beam. The results are presented as a function of
laboratory momentum in 2 intervals of the laboratory polar angle covering the
range from 20 up to 240 mrad. The kaon spectra are compared with predictions of
several hadron production models. Using the published pion results and the new
kaon data, the K+/\pi+ ratios are computed.
