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Bassino et al. (arXiv:1907.08517) have shown that uniform random co-graphs(graphs without induced $P_4$) of size $n$ converge to a certainnon-deterministic graphon. The edge-density of this graphon is a randomvariable $\Lambda \in [0,1]$ whose first moments have been computed by theseauthors. The first purpose of this note is to observe that, in fact, thesemoments 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 theBrownian 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 ${S_k}\simc{\sqrt{k}\log k}$ in probability, with $c=(\sqrt{2\pi})^{-1}$.  The method to establish the recurrence relation is reminiscent of Janson'scomputation of moments of the Wiener index of (large) random trees. Thelogarithm factor in the convergence result comes from the estimation of Riemannsums in which summands are weighted by the integer divisor function -- suchsums naturally occur in the problem. We have not been able to analyse theasymptotics of moments of $\Lambda$ directly from the recurrence relation, andin fact our study of $S_k$ is independent from it. Several things remain to bedone, in particular we only scratch the question of large deviations of $S_k$,and the precise asymptotics of moments of $\Lambda$ is left open.

On the edge-density of the Brownian co-graphon and common ancestors of pairs in the CRT