  Wilf's Sixth Unsolved Problem asks for any interesting properties of the set
of partitions of integers for which the (nonzero) multiplicities of the parts
are all different. We refer to these as \emph{Wilf partitions}. Using $f(n)$ to
denote the number of Wilf partitions, we establish lead-order asymptotics for
$\ln{f(n)}$.
