

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
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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
The following values taken from the Max Horn website are improvements over those given in the ConwayDietrichO'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



CROSSREFS



KEYWORD

nonn,hard,more,nice


AUTHOR



EXTENSIONS

More terms from Victoria A. Sapko (vsapko(AT)canes.gsw.edu), Nov 04 2003
More terms from N. J. A. Sloane, Oct 03 2008, from the John H. Conway, Heiko Dietrich and E. A. O'Brien article.


STATUS

approved



