Calculate Max Number Of Harmonics for given Sample Rate?
No, you don't just multiply by 2, you multiply by every integer.  You can have a 2nd harmonic, a 3rd harmonic, 4th, etc.  (Only multiplying by 2s would tell you the number of octaves, not the number of harmonics.)

So take Nyquist frequency, and divide by the fundamental frequency


  22050 Hz / 20 Hz = 1102.5


Then round down to the nearest integer.  So you can fit 1102 harmonics.  The 1102th harmonic is 1102*20 = 22040 Hz, while the 1103th harmonic is 1103*20 = 22060 Hz, which is too high.

(Note that some consider the fundamental as the 0th harmonic while others consider it the first harmonic.  I am counting it as the first, 1*f.)