Fo is an harmonic component, and it is the first of the sequence, so in my opinion we can call it
h1, and so on, h2, h3,...
In this way their numbering become very obvious and simple, and math help us.
If we consider the octave intervals of the harmonic series, we note that their numbers are:
h1 = Fo, base frequency
h2 = first octave
h4 = second octave
h8 = third octave
h16 = fourth octave
so, obviously
the first octave includes 1 harmonic component
the second octave includes 2 harmonic components
the third octave includes 4 harmonic components
the fourth octave includes 8 harmonic components
Not only, for example the octave of h3 is h6, the octave of h5 is h10, and so on.
it is very obvious but really charming for me!
What do you think?