2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/194762The hierarchy of conformally coupled scalars with the increasing scaling dimensions $Δ_{k}=k-d/2$, $k=1,2,3,... $ connected with the $k$-th Euler density in the corresponding space-time dimensions $d\geq 2k$ is proposed. The corresponding conformal invariant Lagrangian with the $k$-th power of Laplacian for the already known cases $k=1,2$ is reviewed, and the subsequent case of $k=3$ is completely constructed and analyzed.Latex, 11 pages, v.2, two misprints correctedHigh Energy Physics - Theorytext