  We determine the $N_c$--dependence of the resonance contributions to the
Adler--Weisberger sum rule for the inverse square $1/g_A^2$ of the axial charge
coupling constant and show that in the large $N_c$ limit the contributions of
the Roper-like excitations scale as $O(1/N_c)$. Consistency with the $1/N_c^2$
scaling of the $1/g_A^2$ term in the sum rule requires these contributions to
cancel against each other.
