cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A384146 Smallest squarefree order m > 0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists.

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%I A384146 #29 May 29 2025 07:31:02
%S A384146 1,6,609,30,273,42,903,510,8729,3255,494711,210,16951,5115,54431,1218
%N A384146 Smallest squarefree order m > 0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists.
%C A384146 It has been established that every n < 10000000 arises as the number of groups up to isomorphism of some squarefree m. That is, a(n) > 0 for n < 10000000.
%C A384146 It is conjectured that 0 never appears in this sequence.
%H A384146 J. 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>, Math. Intell., Vol. 30, No. 2, Spring 2008.
%e A384146 a(3)=609 since there are 3 groups of order 609 up to isomorphism, and 609 is the smallest squarefree integer such that there are 3 groups of that order.
%Y A384146 Cf. A046057 (m not necessarily squarefree).
%K A384146 nonn,more
%O A384146 1,2
%A A384146 _Robin Jones_, May 21 2025