An interstellar traveller stands upon the surface of an alien planet beneath the light of an unfamiliar sun. The planet upon which he stands orbits one star of a binary system in which one is a G-class yellow dwarf and the other is an M-class red dwarf.
While they are indeed orbiting their common barycentre, the stars are sufficiently distant from one another that the red dwarf companion does not interfere with the orbit of the planet, nor does it contribute sufficient insolation to affect the planet's climate.
My question is this: How close must the companion star be for it to appear noticeably more prominent in the sky compared to background stars?
(My assumption here being that at a certain distance a red dwarf will simply blend in with the stars behind it.)