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 A298910 Numbers n such that there are precisely 19 groups of order n. 2
 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, 50673, 55083, 55629, 57603, 58539, 58695, 60501 (list; graph; refs; listen; history; text; internal format)
 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. Gordon Royle, Numbers of Small Groups FORMULA Sequence is { n | A000001(n) = 19 }. EXAMPLE For n = 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 n such that there are precisely k groups of order n: 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), A249155 (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 A061327 A023062 Adjacent sequences:  A298907 A298908 A298909 * A298911 A298912 A298913 KEYWORD nonn AUTHOR Muniru A Asiru, Jan 28 2018 STATUS approved

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Last modified April 11 15:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)