This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 A198203

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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 22:55 EST 2019. Contains 329974 sequences. (Running on oeis4.)