I don't think the number is defined in LTC. There are rules on the minimum timing of physician visits and NP's can be delegated to take the physician role as long as there is a physician medical director (typically, one every 30 days for first 90 days). Depending on the type of residents seen (i.e., higher percentage of residents with frequent changes in status), the visits can be more frequent as necessary.
I am not sure what you meant by short-term rehab. Are you referring to the 90 day Medicare admission to an LTC? The same rules as above will apply in those cases. Acute in-patient rehab hospitals are different. I worked in one as an NP when I first graduated and the patients are seen everyday so there is a higher need for more providers.