DFT: a function of $n$?
Ah okay thank you. I think what irritated me was that I didn’t consider that the sampled function is a periodic or periodically continued function so that the Fourier transform delivers amplitude values for the base frequency and multiples of it only (so the Fourier transform is discrete), which are indexed as n*(base frequency), so that it is obvious why F „depends“ on n. The amplitude value for n can then be converted into an amplitude value of a frequency given by n*(base frequency) (and the base frequency can be obtained by the period since a signal is only sampled between its starting point and endpoint, whose distance is the period).