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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).
(Formerly M1522 N0596)
1, 2, 5, 19, 132, 3107, 623615, 1834861133, 52976551026562, 12417619575092896741 (list; graph; refs; listen; history; text; internal format)



H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, Semigroup Forum, 14 (1977), 69-79.

R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..10.

Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).

Andreas Distler, Chris Jefferson, Tom Kelsey, Lars Kotthoff, The Semigroups of Order 10, in: M. Milano (Ed.), Principles and Practice of Constraint Programming, 18th International Conference, CP 2012, Qu├ębec 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. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, annotated and scanned copy.

R. J. Plemmons, There are 15973 semigroups of order 6 (annotated and scanned copy)

Eric Weisstein's World of Mathematics, Semigroup.

Index entries for sequences related to semigroups


Column 1 of A058123.

Sequence in context: A273280 A272906 A054926 * A304982 A039719 A332653

Adjacent sequences:  A002783 A002784 A002785 * A002787 A002788 A002789




N. J. A. Sloane


a(8)-a(9) from Andreas Distler, Jan 13 2011

a(10) from Andrey Zabolotskiy, Nov 08 2018



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Last modified April 14 17:43 EDT 2021. Contains 342950 sequences. (Running on oeis4.)