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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 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

K. A. Chandler, Groups formed by redefining multiplication, Canad. Math. Bull. Vol. 31 (4), (1988), 419-423.

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, n-th-power 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, 147-155.

LINKS

Table of n, a(n) for n=1..43.

MathOverflow, Can we color Z^+ with n colors such that a, 2a, …, na all have different colors for all a?

CROSSREFS

Sequence in context: A220160 A183583 A045073 * A234814 A154938 A234100

Adjacent sequences:  A204808 A204809 A204810 * A204812 A204813 A204814

KEYWORD

nonn

AUTHOR

Andres E. Caicedo, Jan 19 2012

STATUS

approved

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Last modified December 10 09:33 EST 2016. Contains 278999 sequences.