%I #41 May 13 2023 23:51:16

%S 675,3267,3549,9947,11475,12625,14283,14749,15525,17745,18875,19575,

%T 22707,24353,31725,35775,38759,39039,39825,41209,43561,45387,49735

%N Numbers m such that there are precisely 17 groups of order m.

%H <a href="/A294949/b294949.txt">Table of n, a(n) for n = 1..23</a>

%H 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 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>

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

%F Sequence is { m | A000001(m) = 17 }.

%e For m = 675, the 17 groups are C675, C225 x C3, C25 x ((C3 x C3) : C3), C25 x (C9 : C3), (C5 x C5) : C27, C135 x C5, C75 x C3 x C3, C9 x ((C5 x C5) : C3), (C45 x C5) : C3, C3 x ((C5 x C5) : C9), ((C5 x C5) : C9) : C3, (C15 x C15) : C3, C45 x C15, C5 x C5 x ((C3 x C3) : C3), C5 x C5 x (C9 : C3), C3 x C3 x ((C5 x C5) : C3), C15 x C15 x C3 where C means Cyclic group and the symbols x and : mean direct and semidirect products respectively.

%p with(GroupTheory): select(n->NumGroups(n)=17, [$1..150001]); # _Muniru A Asiru_, Mar 27 2018

%Y 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), this sequence (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

%K nonn

%O 1,1

%A _Muniru A Asiru_, Nov 11 2017

%E More terms from _Muniru A Asiru_, Nov 17 2017

%E Incorrect terms removed by _Andrew Howroyd_, Jan 28 2022