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A298910
Numbers m such that there are precisely 19 groups of order m.
18
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
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) = 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
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Jan 28 2018
EXTENSIONS
Shortened to remove possibly incorrect terms by Andrew Howroyd, Jan 28 2022
STATUS
approved