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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 14 22:36 EDT 2024. Contains 375167 sequences. (Running on oeis4.)