

A054397


Numbers m such that there are precisely 5 groups of order m.


27



8, 12, 18, 20, 27, 50, 52, 68, 98, 116, 125, 135, 148, 164, 171, 212, 242, 244, 273, 292, 297, 333, 338, 343, 356, 388, 399, 404, 436, 452, 459, 548, 578, 596, 621, 628, 651, 657, 692, 722, 724, 741, 772, 777, 783, 788, 825, 855, 875, 916, 932, 964, 981
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OFFSET

1,1


COMMENTS

For m = 2*p^2 (p prime), there are precisely 5 groups of order m, so A079704 and A143928 (p odd prime) are two subsequences.  Bernard Schott, Dec 10 2021
For m = p^3, p prime, there are also 5 groups of order m, so A030078, where these groups are described, is another subsequence.  Bernard Schott, Dec 11 2021


LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..120 [a(109)a(113) corrected by Georg Fischer, Mar 18 2022]
H. U. Besche, B. Eick and E. A. O'Brien, The Small Groups Library
Gordon Royle, Numbers of Small Groups
Index entries for sequences related to groups


FORMULA

Sequence is { k  A000001(k) = 5 }.  Muniru A Asiru, Nov 03 2017


EXAMPLE

For m = 8, the 5 groups of order 8 are C8, C4 x C2, D8, Q8, C2 x C2 x C2 and for m = 12 the 5 groups of order 12 are C3 : C4, C12, A4, D12, C6 x C2 where C, D, Q mean cyclic, dihedral, quaternion groups of the stated order and A is the alternating group of the stated degree. The symbols x and : mean direct and semidirect products respectively.  Muniru A Asiru, Nov 03 2017


MATHEMATICA

Select[Range[10^4], FiniteGroupCount[#] == 5 &] (* Robert Price, May 23 2019 *)


PROG

(GAP) A054397 := Filtered([1..2015], n > NumberSmallGroups(n) = 5); # Muniru A Asiru, Nov 03 2017


CROSSREFS

Cf. A000001, A003277, A030078, A054395, A054396, A055561, A054397, A079704, A135850, A143928.
Sequence in context: A228056 A187042 A285508 * A075818 A090738 A085103
Adjacent sequences: A054394 A054395 A054396 * A054398 A054399 A054400


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, May 21 2000


EXTENSIONS

More terms from Christian G. Bower, May 25 2000


STATUS

approved



