A390163 - OEIS

%I #8 Jan 08 2026 21:50:17

%S 1,1,2,3,6,14,47,194,1153,10525,164430,4731263

%N Number of nonisomorphic semigroups with n elements satisfying the equation xyz = xy.

%C A semigroup is an associative magma.

%H <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>.

%e The a(4) = 6 semigroups given by their Cayley tables are:

%e   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1

%e   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 1   1 1 1 3   2 2 2 2

%e   1 1 1 1   1 1 1 1   3 3 3 3   3 3 3 3   3 3 3 3   3 3 3 3

%e   1 1 1 1   4 4 4 4   3 3 3 3   4 4 4 4   4 4 4 4   4 4 4 4

%Y Cf. A027851, A362385, A390162, A390165 (labeled case).

%K nonn,more

%O 0,3

%A _Andrew Howroyd_, Nov 18 2025