  We derive the spectrum of Kaluza-Klein descendants of string excitations on
AdS_5 x S^5. String states are organized in long multiplets of the AdS
supergroup SU(2,2|4,R) with a rich pattern of shortenings at the higher spin
enhancement point \lambda=0. The string states holographically dual to the
higher spin currents of SYM theory in the strict zero coupling limit are
identified together with the corresponding Goldstone particles responsible for
the Higgsing of the higher spin symmetry at \lambda\neq 0. Exploiting higher
spin symmetry we propose a very simple yet effective mass formula and establish
a one-to-one correspondence between the complete spectrum of \Delta_0 <= 4
string states and relevant/marginal single-trace deformations in N=4 SYM theory
at large N. To this end, we describe how to efficiently enumerate scaling
operators in `free' YM theory, with the inclusion of fermionic `letters', by
resorting to Polya theory. Comparison between the spectra of 1/4-BPS states is
also presented. Finally, we discuss how to organize the spectrum of N=4 SYM
theory in SU(2,2|4,R) supermultiplets by means of some kind of `Eratostenes's
sieve'.
