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We argue that the conjectural relation between the subleading term in thesmall-squashing expansion of the free energy of general three-dimensional CFTson squashed spheres and the stress-tensor three-point charge $t_4$ proposed inarXiv:1808.02052: $F_{\mathbb{S}^3_{\varepsilon}}^{(3)}(0)=\frac{1}{630}\pi^4C_{\scriptscriptstyle T} t_4$, holds for an infinite family of holographichigher-curvature theories. Using holographic calculations for quartic andquintic Generalized Quasi-topological gravities and general-orderQuasi-topological gravities, we identify an analogous analytic relation betweensuch term and the charges $t_2$ and $t_4$ valid for five-dimensional theories:$F_{\mathbb{S}^5_{\varepsilon}}^{(3)}(0)=\frac{2}{15}\pi^6 C_{\scriptscriptstyle T} \left[1+\frac{3}{40} t_2+\frac{23}{630} t_4\right]$. Wetest both conjectures using new analytic and numerical results forconformally-coupled scalars and free fermions, finding perfect agreement.

Partition functions on slightly squashed spheres and flux parameters