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A005180 Orders of simple groups.
(Formerly M0651)
33
1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 60, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 168, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Officially the group of order 1 is not considered to be simple - see for example Rotman, Group Theory.
REFERENCES
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985.
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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
C. Cato, The orders of the known simple groups as far as one trillion, Math. Comp., 31 (1977), 574-577.
Dept. of Pure Math., Univ. Sheffield, The Classification of Finite Simple Groups
D. Gorenstein, R. Lyons & R. Solomon, The Classification of the Finite Simple Groups, AMS Books Online, Providence RI 1994.
D. Gorenstein, R. Lyons & R. Solomon, The Classification of the Finite Simple Groups, Number 2, AMS Books Online, Providence RI 1996.
R. K. Guy and N. J. A. Sloane, Correspondence, 1988.
R. Solomon, A Brief History Of The Classification Of The Finite Simple Groups, Bull. Amer. Math. Soc. 38 (2001), 315-352.
MATHEMATICA
(* Recomputation from A001034. *)
maxOrder = 7789;
A001034 = Select[Cases[Import["https://oeis.org/A001034/b001034.txt", "Table"], {_, _}][[All, 2]], # <= maxOrder&];
Union[{1}, Prime[Range[PrimePi[maxOrder]]], A001034] (* Jean-François Alcover, Aug 19 2019 *)
CROSSREFS
Cf. A000001, A001228. Union of {1}, A000040 and A001034.
Sequence in context: A054403 A092579 A171028 * A118848 A316903 A171041
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved

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Last modified March 3 20:15 EST 2024. Contains 370512 sequences. (Running on oeis4.)