From: buck@shuksan.math.niu.edu (J. B. Stephen (Buck))
Newsgroups: sci.math
Subject: Re: Number of semigroups of order n
Date: 9 Apr 1998 16:09:11 GMT

There has been some work on this.
The cases up to 6 are classic (from the 50's)
I think Nakamura (?).

I don't have my books here, but a good start
may be Clifford and Preston's "Semigroup Theory"
(Vol. 1, from the American Mathematical Society).
Additionally, Light's associativity test is 
discussed there. This may help you, but 
you've probably come up with it yourself.

Note that it is standard practice to enumerate these 
things up to isomorphism and anti-isomorphism.
Buck

In article <6ggk32$jpt@sv074.SanDiegoCA.NCR.COM>,
Joseph Riel <jsr@sparc.sandiegoca.ncr.com> wrote:
>How may semigroups are there of order n?
>That is, given all nxn cayley tables, how many are associative?