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A002787 Number of semigroups of order n with 2 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

%I A002787 M1802 N0712 #35 Aug 15 2025 04:46:05
%S A002787 2,7,37,216,1780,32652,4665709,12710266442,381279977009776
%N A002787 Number of semigroups of order n with 2 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
%D A002787 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
%D A002787 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002787 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002787 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 A002787 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 Table 3 Total.
%H A002787 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 A002787 H. Juergensen and P. Wick, <a href="/A001423/a001423.pdf">Die Halbgruppen von Ordnungen <= 7</a>, annotated and scanned copy.
%H A002787 R. J. Plemmons, <a href="/A001423/a001423_2.pdf">There are 15973 semigroups of order 6</a> (annotated and scanned copy)
%H A002787 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semigroup.html">Semigroup.</a>
%H A002787 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y A002787 Column 2 of A058123.
%K A002787 nonn,hard,more
%O A002787 2,1
%A A002787 _N. J. A. Sloane_
%E A002787 a(8)-a(9) from _Andreas Distler_, Jan 13 2011
%E A002787 a(10) from _Andrey Zabolotskiy_, Nov 08 2018