  F(4) supergravity, the gauge theory of the exceptional six-dimensional
Anti-de Sitter superalgebra, is coupled to an arbitrary number of vector
multiplets whose scalar components parametrize the quaternionic manifold
$SO(4,n)/SO(4)\times SO(n)$. By gauging the compact subgroup $SU(2)_d \otimes
\cG$, where SU(2)_d is the diagonal subgroup of $SO(4)\simeq SU(2)_L\otimes
SU(2)_R$ (the R-symmetry group of six-dimensional Poincar\'e supergravity) and
$\cG$ is a compact group such that $dim\cG = n$, we compute the scalar
potential which, besides the gauge coupling constants, also depends in non
trivial way on the parameter m associated to a massive 2-form $B_{\mu\nu}$ of
the gravitational multiplet. The potential admits an AdS background for g=3m,
as the pure F(4)-supergravity. We compute the scalar squared masses (which are
all negative) and retrieve the results dictated by AdS_6/CFT_5 correspondence
from the conformal dimensions of boundary operators. The boundary F(4)
superconformal fields are realized in terms of a singleton superfield
(hypermultiplet) in harmonic superspace with flag manifold SU(2)/U(1)=S^2. We
analize the spectrum of short representations in terms of superconformal
primaries and predict general features of the K-K specrum of massive type IIA
supergravity compactified on warped $AdS_6\otimes S^4$.
