  Let m(n) be the number of ordered factorizations of n in factors larger than
1. We prove that for every eps>0 n^{rho} m(n) < exp[(log n)^{1/rho}/(loglog
n)^{1+eps}] holds for all integers n>n_0, while, for a constant c>0, n^{rho}
m(n) > exp[c(log n)^{1/\rho}/(loglog n)^{1/rho}] holds for infinitely many
positive integers n, where rho=1.72864... is the real solution to zeta(rho)=2.
We investigate also arithmetic properties of m(n) and the number of distinct
values of m(n).
