We consider a class of singlet operators ( ϕ 2) n in the three-dimensional O ( N ) model with λ 2 ϕ 6 interaction. Recently [1], the corresponding anomalous dimensions γ 2 n were computed by semiclassical methods and the all-loop result for the leading- n corrections in the small λ limit was found. In this paper, we obtain the six-loop expressions not only for the leading- n contribution but also for the subleading one. While the leading correction confirms the predictions of recent semiclassical calculation, the subleading one is a new result and will serve as a future welcome check for all-loop expressions. As an important by-product of our calculation, we provide a full dependence on n of the four-loop γ 2 n in the O ( N ) case. © 2026 The Authors.