Why do you need primes? Pentax's DA* 16-50mm is a perfect landscape lens. Even weather sealed so you don't have to worry about dust or a few sprinkles! I take mine hiking/backpacking, and rarely feel the desire or need to swap out for a prime. The only downside is the weight on the camera is a little more, although you might save on total weight when considering 3 lenses to cover the same range. Just a thought!
wide when you need it...for those large objects that you can't get away from but still want to capture
normal is great...to capture the amount of a scenery you might be able to visually focus on had you been there
or short tele if you have the feeling to capture some more intimate details
I also have DA15, FA31, and FA43 (which are the approximate focal lengths of these 3 shots), but honestly it's a pain to switch lenses. Unless you are going somewhere and your sole purpose is to take landscape photos and you have plenty of time to do so, switching lenses may seem like hassle. Using one of those lenses instead of the DA* may have made any of those photos technically better (sharper, maybe less distortion...etc), but would not have change the feeling of the photos. The original lighting, composition, etc has the largest effect on a photo.
Aside from that though, to recommend a single focal length as a landscape lens would be difficult. 15mm is too wide for a lot of shots in my opinion, unless you are always in tight spaces or want dramatic perspective. 20mm is pretty good as a general purpose landscape focal length, should be wide enough for most applications but doesn't have that "super-wide" look. 28mm-31mm shots may be more natural pleasing because of the natural perspective that they offer, but I've found that the normal focal length range can be quite limiting in many landscape situations, and you may be forced to do some small panorama stitching (which has it's own set of advantages and disadvantages). Any longer focal length I would have trouble recommending because it gets too tight to capture a lot of scenes without significant stitching.
If you are willing to do small panorama stitching (4-8 photos) to capture scenes requiring wide angle of view, I would recommend a nice lens around 28mm (any of manual pentax lenses would do nicely here for cheap $$). If you don't want to hassle with panos except for the most extreme wide angle needs, I'd go for a 20mm lens (e.g. DA21Ltd)