  For $\Lambda$-$n$-coalescents with mutation, we analyse the size $O_n$ of the
partition block of $i\in\{1,\ldots,n\}$ at the time where the first mutation
appears on the tree that affects $i$ and is shared with any other
$j\in\{1,\ldots,n\}$. We provide asymptotics of $O_n$ for $n\to\infty$ and a
recursion for all moments of $O_n$ for finite $n$. This variable gives an upper
bound for the minimal clade size [2], which is not observable in real data. In
applications to genetics, it has been shown to be useful to lower
classification errors in genealogical model selection [10].
