This paper reports on a curiosity concerning magic numbers in neutral molecular clusters, namely on magic numbers related to the photoelectron anisotropy in angle-resolved photoelectron spectra. With a combination of density functional calculations and experiment, we search for magic numbers in Na(H2O)n, Na(NH3)n, Na(CH3OH)n, and Na(CH3OCH3)n clusters. In clusters of high symmetry, the highest occupied molecular orbital can be delocalized over an extended region, forming a symmetric charge distribution of high s character, which results in a pronounced anisotropy in the photoelectron angular distribution. We find magic numbers at n = 6 and 4 for sodium-doped dimethyl ether and ammonia clusters, respectively, but not for sodium-doped water and methanol clusters, which is likely a consequence of the degree of hydrogen bonding and the number of structural isomers.