  We report the number of semigroups with 9 elements up to isomorphism or
anti-isomorphism to be 52,989,400,714,478 and up to isomorphism to be
105,978,177,936,292. We obtained these results by combining computer search
with recently published formulae for the number of nilpotent semigroups of
degree 3. We further provide a complete account of the automorphism groups of
the semigroups with at most 9 elements. We use this information to deduce that
there are 148,195,347,518,186 distinct associative binary operations on an
8-element set and 38,447,365,355,811,944,462 on a 9-element set.
