  Bassino et al. (arXiv:1907.08517) have shown that uniform random co-graphs
(graphs without induced $P_4$) of size $n$ converge to a certain
non-deterministic graphon. The edge-density of this graphon is a random
variable $\Lambda \in [0,1]$ whose first moments have been computed by these
authors. The first purpose of this note is to observe that, in fact, these
moments can be computed by a simple recurrence relation.
  The problem leads us to the following question of independent interest: given
$k$ i.i.d. uniform pairs of points $(X_1,Y_1),$ $\dots$, $(X_k,Y_k)$ in the
Brownian CRT, what is the size $S_k$ of the set $\{X_i\wedge Y_i, i=1\dots k\}$
formed by their pairwise last common ancestors? We show that ${S_k}\sim
c{\sqrt{k}\log k}$ in probability, with $c=(\sqrt{2\pi})^{-1}$.
  The method to establish the recurrence relation is reminiscent of Janson's
computation of moments of the Wiener index of (large) random trees. The
logarithm factor in the convergence result comes from the estimation of Riemann
sums in which summands are weighted by the integer divisor function -- such
sums naturally occur in the problem. We have not been able to analyse the
asymptotics of moments of $\Lambda$ directly from the recurrence relation, and
in fact our study of $S_k$ is independent from it. Several things remain to be
done, in particular we only scratch the question of large deviations of $S_k$,
and the precise asymptotics of moments of $\Lambda$ is left open.
