login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A046057 Smallest order m > 0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists. 6
1, 4, 75, 28, 8, 42, 375, 510, 308, 90, 140, 88, 56, 16, 24, 100, 675, 156, 1029, 820, 1875, 6321, 294, 546, 2450, 2550, 1210, 2156, 1380, 270, 11774, 630 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
R. Keith Dennis conjectures that there are no 0's in this sequence. See A053403 for details.
In (John H. Conway, Heiko Dietrich and E. A. O'Brien, 2008), m is called the "minimal order attaining n" and is denoted by moa(n). - Daniel Forgues, Feb 15 2017
a(33) > 30500. - Muniru A Asiru, Nov 15 2017
From Jorge R. F. F. Lopes, Jan 07 2022: (Start)
The following values taken from the Max Horn website are improvements over those given in the Conway-Dietrich-O'Brien table (see Links):
a(58) = 3591, a(59) = 6328, a(63) = 2025, a(73) = 24003, a(74) = 25250, a(78) = 12750, a(90) = 2970, a(91) = 2058, a(92) = 15092. (End)
REFERENCES
J. H. Conway et al., The Symmetries of Things, Peters, 2008, p. 209.
LINKS
Hans Ulrich Besche and Bettina Eick, Construction of finite groups, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 387-404.
Hans Ulrich Besche and Bettina Eick, The groups of order at most 1000 except 512 and 768, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 405-413.
John H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, The Mathematical Intelligencer, Volume 30, Issue 2 (2008), pp 6-15, DOI:10.1007/BF02985731.
John H. Conway, Heiko Dietrich and E. A. O'Brien, Table of n, a(n) for n = 1..100 (with some question marks) [contains some errors: see comment from Jorge R. F. F. Lopes].
Steven Finch, The On-Line Encyclopedia of Integer Sequences, founded in 1964 by N. J. A. Sloane, A Tribute to John Horton Conway, The Mathematical Intelligencer (2021) Vol. 43, 146-147.
Eric Weisstein's World of Mathematics, Finite Group.
CROSSREFS
Sequence in context: A007157 A000857 A240007 * A280889 A257367 A072373
KEYWORD
nonn,hard,more,nice
AUTHOR
EXTENSIONS
More terms from Victoria A. Sapko (vsapko(AT)canes.gsw.edu), Nov 04 2003
a(20) corrected by N. J. A. Sloane, Jan 21 2004
More terms from N. J. A. Sloane, Oct 03 2008, from the John H. Conway, Heiko Dietrich and E. A. O'Brien article.
a(31)-a(32) from Muniru A Asiru, Nov 15 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)