As you know, but other readers maybe don't, on Earth the sunlight is scattered by Rayleigh scattering on the molecules of the atmosphere. This has quite a strong wavelength dependence, with blue light being scattered much more efficiently than red light.
On Mars, there is almost no atmosphere. Instead, the Sun's light is scattered by the fine, red dust swirled up in the (thin) air. In the visible spectrum, the scattering properties of this dust happens to have an opposite wavelength dependence than that of the Earth's atmosphere, with a rather low scattering cross section in the blue, rising steeply toward longer wavelengths (e.g. Ockert-Bell et al. 1997).
Thus, the red light is scattered over the Martian sky, creating a red sky, while the blue light passes almost unhindered through, giving the blue Sun.
In addition, the asymmetry parameter of the dust is rather large, meaning that the blue light that is scattered has a preference for being scattered in the forward direction, i.e. toward the observer of the sunset (e.g. Vincendon et al. 2007). This creates a blue halo around the Sun as it sets.
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