A389994 - OEIS

%I #7 Oct 26 2025 17:40:47

%S 2,6,363,30,12,78,605,690,532,132,364,152,60,36,54,126,3267,342,5145,

%T 1220,3249,9075,1014,798,8450,3450,2660,2244,2820,396,25886,1170

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

%H John H. Conway, Heiko Dietrich and E. A. O'Brien, <a href="https://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 Max Horn, <a href="https://groups.quendi.de/">Numbers of isomorphism types of finite groups of given order</a>.

%e a(1) = 2 because A000001(1) = 1 and A000001(2) = 1.

%e a(2) = 6 because A000001(4) = 2 and A000001(6) = 2, and no other values of A000001 below 6 are equal to 2.

%Y Cf. A000001, A046057 (smallest order), A389995 (third smallest order).

%K nonn,hard,more

%O 1,1

%A _Robin Jones_, Oct 21 2025