highly composite number

We call $n$ a highly composite number if $d(n)>d(m)$ for all , where $d(n)$ is the number of divisors of$n$. The first several are 1, 2, 4, 6, 12, 24. The sequence is http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=002182A002182 in Sloane’s OEIS.

The integer $n$ is superior highly composite if there is an $ϵ>0$ such that for all$m\ne n$,

$$d(n)n^{-ϵ}>d(m)m^{-ϵ}.$$

The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360. The sequence is http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=002201A002201 in Sloane’s encyclopedia.