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%I M0651 #32 Aug 19 2019 16:03:19
%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.
%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 R. A. Wilson et al., <a href="http://for.mat.bham.ac.uk/atlas/html">ATLAS of Finite Group Representations</a>
%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_
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