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We report a strong enhancement of the light absorption in single coaxial nanowires (NWs) of Si core/dielectric shells. We have calculated the light absorption coefficient within the framework of the Lorenz-Mie light scattering theory and found out that it is greatly increased by effective light trapping in Si cores owing to dielectric shells, as compared to that in Si NWs. We show that the strong absorption of light stems mainly from off-resonance enhancement and also from resonance contribution. By optimally tuning the core radius, the shell thickness, and the shell refractive index, we have obtained ~102% increase of the photocurrent.