

A204811


Groupless numbers.


0



195, 205, 208, 211, 212, 214, 217, 218, 220, 227, 229, 235, 242, 244, 246, 247, 248, 252, 253, 255, 257, 258, 259, 263, 264, 265, 266, 267, 269, 271, 274, 275, 279, 283, 286, 287, 289, 290, 291, 294, 295, 297, 298
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OFFSET

1,1


COMMENTS

Let [n]={1,..,n}. A number n is groupless iff there is no binary operation . on [n] such that G=([n],.) is a group, and . extends the partial graph of multiplication on [n], i.e., whenever i,j and their usual product i*j are in [n], then i.j=i*j. If n is not groupless, a witness G is sometimes called an FLP group.
The term "groupless" was coined by Thomas Chartier.


LINKS

Table of n, a(n) for n=1..43.
Andrés Eduardo Caicedo, Thomas A. C. Chartier, Péter Pál Pach, Coloring the nsmooth numbers with n colors, arXiv:1902.00446 [math.NT], 2019.
K. A. Chandler, Groups formed by redefining multiplication, Canad. Math. Bull. Vol. 31 (4), (1988), 419423.
Th. A. Ch. Chartier, Coloring problems, MS Thesis in Mathematics, Boise State University, December, 2011.
R. Forcade and A. Pollington, What is special about 195? Groups, nthpower maps and a problem of Graham, in Proceedings of the First Conference of the Canadian Number Theory Association, Banff, 1988, R.A. Mollin, ed., Walter de Gruyter, Berlin, 1990, 147155.
MathOverflow, Can we color Z^+ with n colors such that a, 2a, …, na all have different colors for all a?


CROSSREFS

Sequence in context: A183583 A296893 A045073 * A234814 A154938 A234100
Adjacent sequences: A204808 A204809 A204810 * A204812 A204813 A204814


KEYWORD

nonn


AUTHOR

Andres E. Caicedo, Jan 19 2012


STATUS

approved



