It appears to be the 'fret' number, just as you'd find in the rest of the tab. Except open harmonics start out over frets - 1st is at the 12th fret, an octave, but as the string gets divided more and more, the nodes become out of line with the guitar frets. The 6th harmonic is found over 'fret 2.7' and the 5th over 'fret 3.2'.This is obviously very close to where the fretting hand is working anyway, so convenient to play with just about any finger.
The '15va' gives the fact that the note heard is 2 octaves above the written note.So the 2nd string harmonic is a minor 7th note - A, and the third string harmonic is a P5, of G, which will be D (assuming there's no key sig. on the staff).
There are other places to touch an open string to get a same harmonic. Try the 3rd harmonic, found over 5th fret. There's the same one over the 24th fret. If you haven't got a 24th fret, it's often in line with the neck pup. Or work out where it would have been put.Just a quarter of the way alon the string - from each direction.
The numbers on the tab can be in diamonds too.
Edit: as it happens, Wikipedia has an expanded answer to mine, worth a read !