A005180 - OEIS

%I M0651 #35 Jun 15 2024 17:58:20

%S 1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,60,61,67,71,73,79,

%T 83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,168,

%U 173,179,181,191,193,197,199,211,223,227,229,233,239,241

%N Orders of simple groups.

%C Officially the group of order 1 is not considered to be simple - see for example Rotman, Group Theory.

%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].

%D M. Hall, Jr., A search for simple groups of order less than one million, pp. 137-168 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A005180/b005180.txt">Table of n, a(n) for n = 1..1000</a>

%H M. Aschbacher, <a href="http://www.ams.org/bull/1997-34-01/S0273-0979-97-00703-9/S0273-0979-97-00703-9.pdf">Review of "Classification of the finite simple groups, No. 2" by D. Gorenstein, R. Lyons & R. Solomon</a>

%H C. Cato, <a href="https://doi.org/10.1090/S0025-5718-1977-0430052-X">The orders of the known simple groups as far as one trillion</a>, Math. Comp., 31 (1977), 574-577.

%H Dept. of Pure Math., Univ. Sheffield, <a href="http://www.shef.ac.uk/~puremath/theorems/simple.html">The Classification of Finite Simple Groups</a>

%H D. Gorenstein, R. Lyons & R. Solomon, <a href="http://www.ams.org/online_bks/surv401">The Classification of the Finite Simple Groups</a>, AMS Books Online, Providence RI 1994.

%H D. Gorenstein, R. Lyons & R. Solomon, <a href="http://www.ams.org/online_bks/surv402">The Classification of the Finite Simple Groups, Number 2</a>, AMS Books Online, Providence RI 1996.

%H R. K. Guy and N. J. A. Sloane, <a href="/A005180/a005180.pdf">Correspondence</a>, 1988.

%H R. Solomon, <a href="https://doi.org/10.1090/S0273-0979-01-00909-0">A Brief History Of The Classification Of The Finite Simple Groups</a>, Bull. Amer. Math. Soc. 38 (2001), 315-352.

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%t (* Recomputation from A001034. *)

%t maxOrder = 7789;

%t A001034 = Select[Cases[Import["https://oeis.org/A001034/b001034.txt", "Table"], {_, _}][[All, 2]], # <= maxOrder&];

%t Union[{1}, Prime[Range[PrimePi[maxOrder]]], A001034] (* _Jean-François Alcover_, Aug 19 2019 *)

%Y Cf. A000001, A001228. Union of {1}, A000040 and A001034.

%K nonn,nice,easy

%O 1,2

%A _N. J. A. Sloane_, _R. K. Guy_