cp's OEIS Frontend

A002788 Idempotent semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

%I A002788 M1679 N0661 #27 Feb 16 2025 08:32:26
%S A002788 1,1,2,6,26,135,875,6749,60601,618111,7033090
%N A002788 Idempotent semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
%C A002788 An idempotent semigroup is one whose elements are all idempotents.
%D A002788 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
%D A002788 R. J. Plemmons, Construction and analysis of non-equivalent finite semigroups, pp. 223-228 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
%D A002788 S. Satoh, K. Yama and M. Tokizawa, Semigroups of order 8; Semigroup Forum 49, 1994.
%D A002788 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002788 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002788 Andreas Distler, <a href="http://hdl.handle.net/10023/945">Classification and Enumeration of Finite Semigroups</a>, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).
%H A002788 R. J. Plemmons, <a href="/A001423/a001423_2.pdf">There are 15973 semigroups of order 6</a> (annotated and scanned copy)
%H A002788 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H A002788 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y A002788 Cf. A001423. Main diagonal of A058123.
%K A002788 nonn,nice,hard
%O A002788 0,3
%A A002788 _N. J. A. Sloane_
%E A002788 Additional reference and comments from Michael Somos
%E A002788 a(7) term from _Christian G. Bower_, Feb 19 2001
%E A002788 a(8) (from the Satoh et al. reference) sent by Tom Kelsey (tom(AT)cs.st-and.ac.uk), Jun 17 2008
%E A002788 a(9)-a(10) from _Andreas Distler_, Jan 12 2011