  Apparently convergent contributions of resummed perturbative series at the
next-to-leading order of the 1/N expansion in the O(N) model are reanalyzed in
terms of renormalizability. Compared to our earlier article [G. Fejos et al.,
Phys. Rev. D 80, 025015 (2009)], an additional subtraction is performed. We
show numerically that this is indispensable for diminishing the cutoff
sensitivity of some integrals below the scale of the Landau pole. Following the
method of our earlier article, an improved counterterm Lagrangian is
constructed in the two-particle irreducible formalism, with and without the use
of an auxiliary field formulation.
