  In this paper we continue our research on the concept of liken. This notion
has been defined as a sequence of non-negative real numbers, tending to
infinity and closed with respect to addition in $\mathbb{R}$. The most
important examples of likens are clearly the set of natural numbers
$\mathbb{N}$ with addition and the set of positive natural numbers
$\mathbb{N}^{*}$ with multiplication, represented by a sequence
$(\ln({n+1}))_0^{\infty}$.
  The set of all likens can be parameterized by the points of some infinite
dimensional, complete metric space. In this space of likens we consider
elements up to isomorphism and define properties of likens as such, that are
isomorphism invariant. The main result of this work is a theorem characterizing
the liken ${\mathbb N}^*$ of natural numbers with multiplication in the space
of all likens.
