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It's well known that stars of a higher (i.e. hotter) spectral class have higher luminosities, due to their larger radii and hotter temperatures. Stars of spectral types O through G have no problem standing out in the night sky due to this.

However red dwarfs (class M) are simply too small and cool to be visible to the naked eye, let alone be considered "bright". That leaves class K stars. Googling "bright K-type stars" yields stars such as Pollux and Kochab, and while they technically are K-type stars due to their temperatures, they have far bigger radii than even the largest main-sequence K-type stars and thus aren't really applicable.

So this leaves me with the title question: Are there any bright main-sequence K-type stars in the night sky? “Bright” is subjective, but I think a cap of apparent magnitude 3 is reasonable. Surely there's at least one bright K-type star that isn't a giant, right? And if not, are there any at all that are visible to the naked eye to begin with?

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No.

At 10 light years and at the brighter end of the K stars, Epsilon Eridani is the brightest main sequence K-type star, at magnitude 3.7. No solitary K-type stars are brighter.

Among the stars visible to the naked eye, only Sirus and Alpha Centauri are closer. Now, about Alpha Centauri, it is actually a multiple-star system, and one of the stars, Alpha Centauri B, is a K-type main sequence star. That star would be magnitude 1.3 if it were alone. But it isn't and is outshone by its G-type neighbour.

Other naked-eye K-type stars are Sigma Draconis and Epsilon Indi. Wikipedia has a convenient list of nearby bright stars.

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    $\begingroup$ There are more stars stars closer than Epsilon Eridani than you say. You probably mean that the only stars visible to the naked eye closer than Epsilon Eridani are Alpha Centauri and Sirius. $\endgroup$
    – M. A. Golding
    Commented Dec 16, 2023 at 4:08
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There is one that I can think of, which is Sigma Draconis, but it is far beyond +3 magnitude. According to Wikipedia, its spectra is K0V, and it is indeed a solitary main sequence star. It's 18 lightyears away and has an apparent magnitude of over +4.5, which is significantly dimmer than the Andromeda galaxy - so it isn't the brightest but it's pretty high for a star of its class. But to put it in perspective, our Sun has well over double its intrinsic luminosity.

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