cp's OEIS Frontend

A005591 Number of semigroups of order n with 3 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

%I A005591 M4246 #23 Aug 15 2025 04:46:42
%S A005591 6,44,351,3093,33445,600027,68769167,219587421825
%N A005591 Number of semigroups of order n with 3 idempotents, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
%D A005591 R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.
%D A005591 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005591 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 A005591 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 at the top row of Table 2.
%H A005591 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 A005591 H. Juergensen and P. Wick, <a href="/A001423/a001423.pdf">Die Halbgruppen von Ordnungen <= 7</a>, annotated and scanned copy.
%H A005591 <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>
%Y A005591 Column 3 of A058123.
%K A005591 nonn
%O A005591 3,1
%A A005591 _N. J. A. Sloane_
%E A005591 a(8)-a(9) from _Andreas Distler_, Jan 13 2011
%E A005591 a(10) from _Andrey Zabolotskiy_, Nov 08 2018