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 A135850 Numbers n such that there are precisely 6 groups of order n. 20
 42, 78, 110, 114, 147, 186, 222, 225, 258, 310, 366, 402, 406, 410, 438, 474, 506, 507, 525, 582, 602, 610, 618, 654, 710, 735, 762, 834, 906, 942, 975, 978, 994, 1010, 1083, 1086, 1089, 1158, 1194, 1266, 1310, 1338, 1374, 1378, 1425, 1446, 1474, 1510, 1582 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let gnu(n) = A000001(n) denote the "group number of n" defined in A000001 or in (J. H. Conway, Heiko Dietrich and E. A. O'Brien, 2008), then the sequence n -> gnu(a(n)) -> gnu(gnu(a(n))) -> gnu(gnu(gnu(a(n)))) consists of 1's. - Muniru A Asiru, Nov 19 2017 LINKS Muniru A Asiru, Table of n, a(n) for n = 1..91 J. H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, Math. Intell., Vol. 30, No. 2, Spring 2008. FORMULA Sequence is { k | A000001(k) = 6 }. - Muniru A Asiru, Nov 04 2017 EXAMPLE For n = 42, the 6 groups of order 42 are (C7 : C3) : C2, C2 x (C7 : C3), C7 x S3, C3 x D14, D42, C42 and for n = 78 the 6 groups of order 78 are (C13 : C3) : C2, C2 x (C13 : C3), C13 x S3, C3 x D26, D78, C78 where C, D mean Cyclic, Dihedral groups of the stated order and S is the Symmetric group of the stated degree. The symbols x and : mean direct and semidirect products respectively. - Muniru A Asiru, Nov 04 2017 MATHEMATICA Select[Range[10^4], FiniteGroupCount[#] == 6 &] (* Robert Price, May 23 2019 *) PROG (GAP) A135850 := Filtered([1..2015], n -> NumberSmallGroups(n) = 6); # Muniru A Asiru, Nov 04 2017 CROSSREFS Cf. A000001, A003277, A054395, A054396, A054397, A135850. Sequence in context: A072326 A068700 A303283 * A250381 A153644 A172437 Adjacent sequences:  A135847 A135848 A135849 * A135851 A135852 A135853 KEYWORD nonn AUTHOR N. J. A. Sloane, based on a suggestion from Neven Juric, Mar 08 2008 STATUS approved

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)