A002788 - OEIS

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A002788

Idempotent semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).
(Formerly M1679 N0661)

1, 1, 2, 6, 26, 135, 875, 6749, 60601, 618111, 7033090 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`An idempotent semigroup is one whose elements are all idempotents.`
	REFERENCES	`R. J. Plemmons, There are 15973 semigroups of order 6, Math. Algor., 2 (1967), 2-17; 3 (1968), 23.` `R. J. Plemmons, Construction and analysis of non-equivalent finite semigroups, pp. 223-228 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.` `S. Satoh, K. Yama and M. Tokizawa, Semigroups of order 8; Semigroup Forum 49, 1994.` `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).`
	LINKS	`Andreas Distler, Classification and Enumeration of Finite Semigroups, A Thesis Submitted for the Degree of PhD, University of St Andrews (2010).` `Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.` `Index entries for sequences related to semigroups`
	CROSSREFS	`Cf. A001423. Main diagonal of A058123.` `Sequence in context: A159667 A030957 A030898 * A134094 A009575 A180891` `Adjacent sequences: A002785 A002786 A002787 * A002789 A002790 A002791`
	KEYWORD	`nonn,nice,hard`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com).`
	EXTENSIONS	`Additional reference and comments from Michael Somos.` `a(7) term from Christian G. Bower (bowerc(AT)usa.net), Feb 19 2001` `a(8) (from the Satoh et al. reference) sent by Tom Kelsey (tom(AT)cs.st-and.ac.uk), Jun 17 2008` `a(9)-a(10) from Andreas Distler (andreas(AT)mcs.st-andrews.ac.uk), Jan 12 2011`

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Last modified February 18 00:14 EST 2012. Contains 206085 sequences.