Maybe you have a picture of the lens mount, or you can look at it in person? If it is just a metal screw, then it is m42 and needs adapter. If it is a K-mount bayonet, then you will not need adapter. The K-mount bayonet should look very similar to the K-mount of your other lenses that work on K200D.
Is this the lens?
Vivitar Series 1 (Komine) 28-90mm F2.8-3.5 Lens Reviews - Vivitar Lenses - Pentax Lens Review Database
Apparently this lens comes in different mounts, so make sure the specific one you are buying is K-mount. If it is m42, you need adapter. Again, I suggest you look at it.