The hydration of gas phase Na+ ions produced by electrospray ionization was investigated via high resolution time-of-flight mass spectrometry. Water clusters with up to 80 H2O units have been observed with attention to special peculiarities of mass peaks and structures in the envelope of the mass spectra. For solvated Na+-ions no particularly prominent peaks corresponding to "magic numbers" have been observed in the spectra. In addition, the mass spectra of Na+(H2O)(n) aggregates are compared with those of the H3O+(H2O)(n) system. As a very first step towards a theoretical understanding of the intensities of the experimental mass spectra we have calculated global minimum structures for the Na+(H2O)(n) system with n=4-25, using global geometry optimization methods and a simple model potential for this system. Structural and energetic trends and the systematic build-up of solvent shells of the clusters were studied. Within our simple theoretical model we have not observed (symmetric) clathratelike structures with a central Na+-ion inside as global minimum structures. Instead, a structural transition for n between 17 and 18 water units was found, in agreement with the experimental observations. The unimportance of clathratelike structures and the competition between the two structural principles discovered in this work are proposed as an explanation for the notorious lack of "magic" numbers in the mass spectrum of Na+(H2O)(n) clusters.