A298910 Numbers m such that there are precisely 19 groups of order m.

1029, 5145, 6591, 7803, 8001, 11319, 11739, 12789, 17157, 17493, 20577, 21567, 23667, 23877, 27993, 31311, 32955, 33411, 34671, 34713, 39015, 39753, 40005, 42189, 42861, 45675, 47691, 48363, 49833

Offset

1,1

Links

Table of n, a(n) for n=1..29.

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

Index entries for sequences related to groups

Formula

Sequence is { m | A000001(m) = 19 }.

Example

For m = 1029, the 19 groups are C1029, C147 x C7, C3 x ((C7 x C7) : C7), C3 x (C49 : C7), C21 x C7 x C7, C343 : C3, C49 x (C7 : C3), C7 x (C49 : C3), (C49 x C7) : C3, (C49 x C7) : C3, ((C7 x C7) : C7) : C3, ((C7 x C7) : C7) : C3, ((C7 x C7) : C7) : C3, (C49 : C7) : C3, C7 x ((C7 x C7) : C3), C7 x ((C7 x C7) : C3), (C7 x C7 x C7) : C3, (C7 x C7 x C7) : C3, C7 x C7 x (C7 : C3) where C means the Cyclic group of the stated order and the symbols x and : mean direct and semidirect products respectively.

Maple

with(GroupTheory):
for n from 1 to 3*10^5 do if NumGroups(n) = 19 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), this sequence (k=19), A298911 (k=20).

Sequence in context: A045031 A250759 A260607 * A256075 A351673 A061327

Adjacent sequences: A298907 A298908 A298909 * A298911 A298912 A298913

Keyword

nonn

Author

Muniru A Asiru, Jan 28 2018

Extensions

Shortened to remove possibly incorrect terms by Andrew Howroyd, Jan 28 2022

Status

approved