1,1

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..237

H. U. Besche, B. Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.

Gordon Royle, Numbers of Small Groups

Sequence is { m | A000001(m) = 20 }.

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.

with(GroupTheory):

for n from 1 to 10^4 do if NumGroups(n) = 20 then print(n); fi; od;

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).

Sequence in context: A043805 A043813 A043822 * A279796 A285022 A037999

Adjacent sequences: A298908 A298909 A298910 * A298912 A298913 A298914

Muniru A Asiru, Jan 28 2018

approved