# Could you give a definition of what is a superior highly composite number using only words?

I know very well what is a superior highly composite number, but I would like to see how could we (roughly) define what is a superior highly composite number using only words (using no equations and no inequalities).

The only such definition I've seen is this one found on Wikipedia:

A superior highly composite number is a natural number which has more divisors than any other number scaled relative to the number itself.

• If it wasn't for the exponent $\epsilon$ you could say "A superior highly composite number is a number which is divided by a greater fraction of the numbers less than or equal to it than any smaller number." But the exponent seems to defeat any attempts at clear phrasing. – hobbs Sep 6 '14 at 23:32
• Their definition isn't a very good solution of the exponent problem. I think the problem with using no symbols at all is that it's nearly impossible to convey that we're speaking about a single constant $\epsilon$ for each $n$ and all $k<n$, rather than a different constant for each $k$. – Jaycob Coleman Feb 15 '15 at 22:43

• in the $1^{st}$  competition:   ... to the competing number itself
• in the $2^{nd}$ competition:   ... to the square of the competing number
• in the $3^{rd}$  competition:  ... to the cube of the competing number
• wait what about the competitions where the competing numbers are taken to the exponent of a non-whole number for example $n^{1.5}$ or $n^{3.27913452218237...}$ etc. – ray lin Jun 16 '18 at 20:32