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We present the measurements of the photoionization cross sections of the excited 1 P 1 and 3 S 1 states of ultracold 88 Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the 1 S 0 - 3 P 0 clock transition. The photoionization cross section of the 1 P 1 state is determined from the measured ionization rates of 88 Sr in the magneto-optical trap in the 1 P 1 state to be 2.20(50)×10 -20 m 2 , while the photoionization cross section of 88 Sr in the 3 S 1 state is inferred from the photoionization-induced reduction in the number of atoms transferred through the 3 S 1 state in an operating optical lattice clock to be 1.38(66) ×10 -18 m 2 . Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionization induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionization induced losses for the 3 S 1 state would make the use of the 3 S 1 state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used 3 D 1,2 states during the detection part of the optical clock cycle.