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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).
(Formerly M4246)
6, 44, 351, 3093, 33445, 600027, 68769167, 219587421825 (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 and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=3..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 at the top row of Table 2.

H. Juergensen and P. Wick, Die Halbgruppen von Ordnungen <= 7, annotated and scanned copy.

Index entries for sequences related to semigroups


Column 3 of A058123.

Sequence in context: A115969 A082412 A108452 * A052204 A147688 A090442

Adjacent sequences:  A005588 A005589 A005590 * A005592 A005593 A005594




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 January 24 05:51 EST 2019. Contains 319415 sequences. (Running on oeis4.)