  In this short note, we show that the number of monogenic submonoids of the
full transformation monoid of degree $n$ for $n > 0$, equals the sum of the
number of cyclic subgroups of the symmetric groups on $1$ to $n$ points. We
also prove an analogous statement for monogenic subsemigroups of the finite
full transformation monoids, as well as monogenic inverse submonoids and
subsemigroups of the finite symmetric inverse monoids.
