A390165 - OEIS

%I #11 Jan 08 2026 21:50:13

%S 1,1,3,10,65,856,17497,554632,29533905,2782465840,486675409841,

%T 167183253706624

%N Number of labeled 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) = 65 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

%e     (4)       (12)      (12)      (12)      (24)      (1)

%Y Cf. A023814, A362386, A389829, A390163 (unlabeled version).

%K nonn,more

%O 0,3

%A _Andrew Howroyd_, Nov 27 2025