cp's OEIS Frontend

A298911 Numbers m such that there are precisely 20 groups of order m.

%I A298911 #17 May 14 2023 02:31:58
%S A298911 820,1220,1530,2020,2070,2610,2756,3366,3620,4230,4550,4770,4820,5310,
%T A298911 5620,5742,5950,6370,6650,7038,7470,8010,8020,8050,8118,8164,8330,
%U A298911 8420,8874,9220,9306,9310,9316,9630,10170,10420,10494,10820,11050
%N A298911 Numbers m such that there are precisely 20 groups of order m.
%H A298911 Jorge R. F. F. Lopes, <a href="/A298911/b298911.txt">Table of n, a(n) for n = 1..237</a>
%H A298911 H. U. Besche, B. Eick and E. A. O'Brien, <a href="http://dx.doi.org/10.1142/S0218196702001115">A Millennium Project: Constructing Small Groups</a>, Internat. J. Algebra and Computation, 12 (2002), 623-644.
%H A298911 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A298911 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A298911 Sequence is { m | A000001(m) = 20 }.
%e A298911 For m = 820, the 20 groups are (C41 : C5) : C4, C4 x (C41 : C5), C41 x (C5 : C4), C5 x (C41 : C4), C205 : C4, C820, (C41 : C5) : C4, C2 x ((C41 : C5) : C2), C2 x C2 x (C41 : C5), C5 x (C41 : C4), C41 x (C5 : C4), C205 : C4, C205 : C4, C205 : C4, C205 : C4, D10 x D82, C10 x D82, C82 x D10, D820, C410 x C2 where C, D mean the Cyclic, Dihedral groups of the stated order and the symbols x and : mean direct and semidirect products respectively.
%p A298911 with(GroupTheory):
%p A298911 for n from 1 to 10^4 do if NumGroups(n) = 20 then print(n); fi; od;
%Y A298911 Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), this sequence (k=20).
%K A298911 nonn
%O A298911 1,1
%A A298911 _Muniru A Asiru_, Jan 28 2018