In recent literature, one-loop tests of the higher-spin AdS

${}_{d+1}$ /CFT

${}_{d}$ correspondences were carried out. Here, we extend these results to a more general set of theories in

$d>2$ . First, we consider the Type B higher spin theories, which have been conjectured to be dual to CFTs consisting of the singlet sector of

*N* free fermion fields. In addition to the case of

*N* Dirac fermions, we carefully study the projections to Weyl, Majorana, symplectic and Majorana–Weyl fermions in the dimensions where they exist. Second, we explore theories involving elements of both Type A and Type B theories, which we call Type AB. Their spectrum includes fields of every half-integer spin, and they are expected to be related to the

$U\left(N\right)/O\left(N\right)$ singlet sector of the CFT of

*N* free complex/real scalar and fermionic fields. Finally, we explore the Type C theories, which have been conjectured to be dual to the CFTs of

*p*-form gauge fields, where

$p=\frac{d}{2}-1$ . In most cases, we find that the free energies at

$O\left({N}^{0}\right)$ either vanish or give contributions proportional to the free-energy of a single free field in the conjectured dual CFT. Interpreting these non-vanishing values as shifts of the bulk coupling constant

${G}_{N}\sim 1/(N-k)$ , we find the values

$k=-1,-1/2,0,1/2,1,2$ . Exceptions to this rule are the Type B and AB theories in odd

*d*; for them, we find a mismatch between the bulk and boundary free energies that has a simple structure, but does not follow from a simple shift of the bulk coupling constant.

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