login
A298911
Numbers m such that there are precisely 20 groups of order m.
19
820, 1220, 1530, 2020, 2070, 2610, 2756, 3366, 3620, 4230, 4550, 4770, 4820, 5310, 5620, 5742, 5950, 6370, 6650, 7038, 7470, 8010, 8020, 8050, 8118, 8164, 8330, 8420, 8874, 9220, 9306, 9310, 9316, 9630, 10170, 10420, 10494, 10820, 11050
OFFSET
1,1
LINKS
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.
FORMULA
Sequence is { m | A000001(m) = 20 }.
EXAMPLE
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.
MAPLE
with(GroupTheory):
for n from 1 to 10^4 do if NumGroups(n) = 20 then print(n); fi; od;
CROSSREFS
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
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Jan 28 2018
STATUS
approved