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A046057 Smallest order m>0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists. 6

%I

%S 1,4,75,28,8,42,375,510,308,90,140,88,56,16,24,100,675,156,1029,820,

%T 1875,6321,294,546,2450,2550,1210,2156,1380,270,11774,630

%N Smallest order m>0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists.

%C R. Keith Dennis conjectures that there are no 0's in this sequence. See A053403 for details.

%C 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

%C a(33) > 30500. - _Muniru A Asiru_, Nov 15 2017

%D J. H. Conway et al., The Symmetries of Things, Peters, 2008, p. 209.

%H H. U. Besche, <a href="https://www.gap-system.org/Packages/sgl.html">The Small Groups library</a>

%H Hans Ulrich Besche and Bettina Eick, <a href="https://doi.org/10.1006/jsco.1998.0258">Construction of finite groups</a>, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 387-404.

%H Hans Ulrich Besche and Bettina Eick, <a href="https://doi.org/10.1006/jsco.1998.0259">The groups of order at most 1000 except 512 and 768</a>, Journal of Symbolic Computation, Vol. 27, No. 4, Apr 15 1999, pp. 405-413.

%H John H. Conway, Heiko Dietrich and E. A. O'Brien, <a href="http://www.math.auckland.ac.nz/~obrien/research/gnu.pdf">Counting groups: gnus, moas and other exotica</a>, The Mathematical Intelligencer, Volume 30, Issue 2 (2008), pp 6-15, DOI:<a href="https://doi.org/10.1007/BF02985731">10.1007/BF02985731</a>.

%H John H. Conway, Heiko Dietrich and E. A. O'Brien, <a href="/A046057/a046057.txt">Table of n, a(n) for n = 1..100 (with some question marks)</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FiniteGroup.html">Finite Group.</a>

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

%Y Cf. A000001, A046056, A046058, A046059, A053403.

%K nonn,hard,more,nice,changed

%O 1,2

%A _Eric W. Weisstein_

%E More terms from Victoria A. Sapko (vsapko(AT)canes.gsw.edu), Nov 04 2003

%E a(20) corrected by _N. J. A. Sloane_, Jan 21 2004

%E More terms from _N. J. A. Sloane_, Oct 03 2008, from the John H. Conway, Heiko Dietrich and E. A. O'Brien article.

%E a(31)-a(32) from _Muniru A Asiru_, Nov 15 2017

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Last modified June 22 20:06 EDT 2021. Contains 345388 sequences. (Running on oeis4.)