  Vasiliev's type A higher spin theories in AdS4 have been conjectured to be
dual to the U(N) or O(N) singlet sectors in 3-d conformal field theories with
N-component scalar fields. We compare the O(N^0) correction to the 3-sphere
free energy F in the CFTs with corresponding calculations in the higher spin
theories. This requires evaluating a regularized sum over one loop vacuum
energies of an infinite set of massless higher spin gauge fields in Euclidean
AdS4. For the Vasiliev theory including fields of all integer spin and a scalar
with Delta=1 boundary condition, we show that the regularized sum vanishes.
This is in perfect agreement with the vanishing of subleading corrections to F
in the U(N) singlet sector of the theory of N free complex scalar fields. For
the minimal Vasiliev theory including fields of only even spin, the regularized
sum remarkably equals the value of F for one free real scalar field. This
result may agree with the O(N) singlet sector of the theory of N real scalar
fields, provided the coupling constant in the Vasiliev theory is identified as
G_N ~ 1/(N-1). Similarly, consideration of the USp(N) singlet sector for N
complex scalar fields, which we conjecture to be dual to the husp(2;0|4)
Vasiliev theory, requires G_N ~ 1/(N+1). We also test the higher spin AdS3/CFT2
conjectures by calculating the regularized sum over one loop vacuum energies of
higher spin fields in AdS3. We match the result with the O(N^0) term in the
central charge of the W_N minimal models; this requires a certain truncation of
the CFT operator spectrum so that the bulk theory contains two real scalar
fields with the same boundary conditions.
