  Recent studies of holographic properties of massless higher-order gravities,
whose linear spectrum contains only the (massless) graviton, yielded some
universal relations in $d=4$ dimensions between the holographic $a$, $c$
charges and the overall coefficient factor ${\cal C}_T$ of the energy-momentum
tensor two-point function, namely $c=\frac{1}{d-1} \ell\frac{\partial
a}{\partial \ell}={\cal C}_T$, where $\ell$ is the AdS radius. The second
equality was shown to be valid in all dimensions. In this paper, we establish
the first equality in $d=6$ by examining these quantities from $D=7$
higher-order gravities. Consequently the overall coefficient of the two-point
function of the energy-momentum tensor is proportional to this $c$ charge,
generalizing the well-known $d=4$ result. We identify the relevant $c$ charge
as the coefficient of a specific combination of the three type-B anomalies.
Modulo total derivatives, this combination involves Riemann tensor at most
linearly.
