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A002786 Semigroups of order n with 1 idempotent, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

%I A002786 M1522 N0596 #30 Aug 15 2025 04:45:29
%S A002786 1,2,5,19,132,3107,623615,1834861133,52976551026562,
%T A002786 12417619575092896741
%N A002786 Semigroups of order n with 1 idempotent, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
%D A002786 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
%D A002786 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002786 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002786 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 A002786 Andreas Distler, Chris Jefferson, Tom Kelsey, Lars Kotthoff, <a href="https://doi.org/10.1007/978-3-642-33558-7_63">The Semigroups of Order 10</a>, in: M. Milano (Ed.), Principles and Practice of Constraint Programming, 18th International Conference, CP 2012, Québec City, QC, Canada, October 8-12, 2012, Proceedings (LNCS, volume 7514), pp. 883-899, Springer-Verlag Berlin Heidelberg 2012. a(10) is the sum of entries of Tables 4 and 5; note that Table 4 has incorrect Total.
%H A002786 H. Juergensen and P. Wick, <a href="https://gdz.sub.uni-goettingen.de/id/PPN362162808_0014">Die Halbgruppen von Ordnungen <= 7</a>, Semigroup Forum, 14 (1977), 69-79.
%H A002786 H. Juergensen and P. Wick, <a href="/A001423/a001423.pdf">Die Halbgruppen von Ordnungen <= 7</a>, annotated and scanned copy.
%H A002786 R. J. Plemmons, <a href="/A001423/a001423_2.pdf">There are 15973 semigroups of order 6</a> (annotated and scanned copy)
%H A002786 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H A002786 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y A002786 Column 1 of A058123.
%K A002786 nonn,nice,hard
%O A002786 1,2
%A A002786 _N. J. A. Sloane_
%E A002786 a(8)-a(9) from _Andreas Distler_, Jan 13 2011
%E A002786 a(10) from _Andrey Zabolotskiy_, Nov 08 2018