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The Monte Carlo code FLUKA is used to simulate the production of a number of positron emitting radionuclides, ¹⁸F, ¹³N, ⁹⁴Tc, ⁴⁴Sc, ⁶⁸Ga, ⁸⁶Y, ⁸⁹Zr, ⁵²Mn, ⁶¹Cu and ⁵⁵Co, on a small medical cyclotron with a proton beam energy of 13 MeV. Experimental data collected at the TR13 cyclotron at TRIUMF agree within a factor of 0.6 ± 0.4 with the directly simulated data, except for the production of ⁵⁵Co, where the simulation underestimates the experiment by a factor of 3.4 ± 0.4. The experimental data also agree within a factor of 0.8 ± 0.6 with the convolution of simulated proton fluence and cross sections from literature. Overall, this confirms the applicability of FLUKA to simulate radionuclide production at 13 MeV proton beam energy.