The photoabsorption spectra of a continuous series of Na(n) clusters (n<or=14, n=20, n=40) have been calculated using a time-dependent density-functional scheme. Accordingly, we present these spectra and show that they are in very good agreement with other theoretically and experimentally obtained photoabsorption spectra. Furthermore, we discuss the influence of the cluster structure on the photoabsorption spectrum for some selected clusters and present for several cluster sizes photoabsorption spectra of different geometrical isomers. The spectra of clusters with five or more atoms are dominated by a few large peaks which can be interpreted as collective plasmon excitations.