A003277 -id:A003277 - cp's OEIS frontend

A249555 Numbers m such that there are precisely 12 groups of order m.

88, 152, 184, 196, 204, 210, 248, 330, 344, 348, 376, 390, 462, 472, 484, 492, 536, 568, 570, 632, 636, 664, 714, 770, 824, 856, 858, 966, 1016, 1048, 1068, 1110, 1112, 1208, 1212, 1230, 1254, 1290, 1304, 1326, 1336, 1356, 1430, 1432, 1444, 1518, 1528, 1592, 1644

Offset: 1

N. J. A. Sloane, Nov 01 2014

nonn

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..1512
Index entries for sequences related to groups

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), this sequence (k=12), A292896 (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A249555 := Filtered([1..2015], n -> NumberSmallGroups(n) = 12); # Muniru A Asiru, Oct 16 2017

Select[Range@ 2074, FiniteGroupCount@ # == 12 &] (* Michael De Vlieger, Oct 16 2017. Note: extending the range to 2075 and further will result in incorrect output. - Andrey Zabolotskiy, Oct 27 2017 *)

A292896 Numbers m such that there are precisely 13 groups of order m.

Original entry on oeis.org

56, 60, 150, 189, 441, 726, 837, 945, 1012, 1161, 1204, 1521, 1575, 1647, 1734, 1809, 1988, 2079, 2133, 2205, 2366, 2619, 2781, 2925, 2948, 3174, 3213, 3556, 3610, 3753, 4077, 4239, 4324, 4347, 4851, 5046, 5211, 5697, 5805, 5908, 6021, 6183, 6507, 6692, 7479, 7497, 7605, 7623, 7641, 7749, 8410, 8451

Offset: 1

Muniru A Asiru, Oct 23 2017

nonn

			The 13 groups of order 56 have the following structure C7 : C8, C56, C7 : Q8, C4 x D14, D56, C2 x (C7 : C4), (C14 x C2) : C2, C28 x C2, C7 x D8, C7 x Q8, (C2 x C2 x C2) : C7, C2 x C2 x D14, C14 x C2 x C2 where C, D and Q mean Cyclic group, Dihedral group and Quarternion group of the stated order. The symbols x and : mean direct and semidirect products respectively.

Muniru A Asiru, Table of n, a(n) for n = 1..273
Gordon Royle, Numbers of Small Groups
H. U. Besche, B. Eick and E. A. O'Brien. The Small Groups Library
Index entries for sequences related to groups

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), this sequence (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A292896 := Filtered([1..2015], n -> NumberSmallGroups(n) = 13);

More terms from Muniru A Asiru, Nov 18 2017

A249550 Numbers m such that there are precisely 7 groups of order m.

Original entry on oeis.org

375, 605, 903, 1705, 2255, 2601, 2667, 3081, 3355, 3905, 3993, 4235, 4431, 4515, 4805, 5555, 6123, 6355, 6375, 6765, 7077, 7205, 7865, 7917, 7959, 8305, 8405, 8625, 8841, 9455, 9723, 9933, 9955, 10285, 10505, 10875, 11005, 11487, 11495, 11571, 11605, 11715, 11935, 12207, 12505, 13005, 13053, 13251, 13255, 13335, 13805, 14133

Offset: 1

N. J. A. Sloane, Nov 01 2014

nonn

			For m = 375, the 7 groups are C375, ((C5 x C5) : C5) : C3, C75 x C5, C3 x ((C5 x C5) : C5), C3 x (C25 : C5), C5 x ((C5 x C5) : C3), C15 x C5 x C5 and for n = 605 the 7 groups are C121 : C5, C605, C11 x (C11 : C5), (C11 x C11) : C5, (C11 x C11) : C5, (C11 x C11) : C5, C55 x C11, where C means Cyclic group and the symbols x and : mean direct and semidirect products respectively. - _Muniru A Asiru_, Nov 11 2017

Muniru A Asiru, Table of n, a(n) for n = 1..198
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

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), this sequence (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), A298910 (k=19), A298911 (k=20).

Warning: The Mma command Select[Range[10^5], FiniteGroupCount[#]==7 &]  gives wrong answers, since FiniteGroupCount[2601] does not return 7. - N. J. A. Sloane, Apr 11 2020

Sequence is { m | A000001(m) = 7 }. - Muniru A Asiru, Nov 11 2017

More terms from Muniru A Asiru, Oct 22 2017

Missing terms added by Muniru A Asiru, Nov 12 2017

A294155 Numbers m such that there are precisely 14 groups of order m.

Original entry on oeis.org

16, 36, 40, 104, 232, 296, 351, 424, 488, 808, 872, 1125, 1192, 1197, 1256, 1384, 1448, 1576, 1755, 1832, 2152, 2216, 2223, 2331, 2344, 2536, 2625, 2792, 2984, 3112, 3176, 3368, 3688, 3861, 4072, 4328, 4329, 4456, 4599, 4875, 4904, 5115, 5187, 5224, 5288, 5301

Offset: 1

Muniru A Asiru, Oct 24 2017

nonn

			For m = 16, the 14 groups of order 16 are C16, C4 x C4, (C4 x C2) : C2, C4 : C4, C8 x C2, C8 : C2, D16, QD16, Q16, C4 x C2 x C2, C2 x D8, C2 x Q8, (C4 x C2) : C2, C2 x C2 x C2 x C2  and for n = 36 the 14 groups of order 36 are C9 : C4, C36, (C2 x C2) : C9, D36, C18 x C2, C3 x (C3 : C4), (C3 x C3) : C4, C12 x C3, (C3 x C3) : C4, S3 x S3, C3 x A4, C6 x S3, C2 x ((C3 x C3) : C2), C6 x C6 where C, D, Q  mean Cyclic group, Dihedral group, Quaternion group of the stated order and S is the Symmetric group of the stated degree. The symbols x and : mean direct and semi-direct products respectively.

Muniru A Asiru, Table of n, a(n) for n = 1..377
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

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), this sequence (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A294155 := Filtered([1..2015], n -> NumberSmallGroups(n) = 14);

A294156 Numbers m such that there are precisely 15 groups of order m.

Original entry on oeis.org

24, 54, 81, 84, 136, 220, 228, 250, 260, 328, 340, 372, 513, 516, 580, 584, 620, 625, 686, 712, 740, 776, 804, 884, 891, 904, 948, 999, 1060, 1096, 1236, 1375, 1377, 1420, 1460, 1508, 1524, 1544, 1668, 1780, 1812, 1863, 1864, 1911, 1924, 1928, 1940, 1956, 1971, 1972, 2056, 2132, 2180

Offset: 1

Muniru A Asiru, Oct 24 2017

nonn

			For m = 24, the 15 groups of order 24 are C3 : C8, C24, SL(2,3), C3 : Q8, C4 x S3, D24, C2 x (C3 : C4), (C6 x C2) : C2, C12 x C2, C3 x D8, C3 x Q8, S4, C2 x A4, C2 x C2 x S3, C6 x C2 x C2 and for n = 54 the 15 groups of order 54 are D54, C54, C3 x D18, C9 x S3, ((C3 x C3) : C3) : C2, (C9 : C3) : C2, (C9 x C3) : C2, ((C3 x C3) : C3) : C2, C18 x C3, C2 x ((C3 x C3) : C3), C2 x (C9 : C3), C3 x C3 x S3, C3 x ((C3 x C3) : C2), (C3 x C3 x C3) : C2, C6 x C3 x C3 where C, D, Q, S, A and SL mean Cyclic, Dihedral, Quaternion, Symmetric, Alternating and Special Linear group. The symbols x and : mean direct and semi-direct products respectively.

Muniru A Asiru, Table of n, a(n) for n = 1..1061
H. U. Besche, B. Eick and E. A. O'Brien, The Small Groups Library
Gordon Royle, Small Even Order Groups [archived copy]
Index entries for sequences related to groups

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), this sequence (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A294156 := Filtered([1..2015], n -> NumberSmallGroups(n) = 15);

Select[ Range@2000, FiniteGroupCount@# == 15 &] (* Robert G. Wilson v, Oct 24 2017 *)

A294156 = { m | A000001(m) = 15 }. - M. F. Hasler, Oct 24 2017

A295161 Numbers m such that there are precisely 16 groups of order m.

Original entry on oeis.org

100, 126, 234, 405, 550, 558, 676, 774, 812, 1098, 1156, 1206, 1218, 1422, 1550, 1746, 1854, 2050, 2502, 2530, 2718, 2826, 2842, 2943, 2982, 3050, 3164, 3364, 3474, 3550, 3798, 3875, 3916, 4014, 4122, 4134, 4214, 4275, 4338, 4401, 4746, 4986, 5094, 5476, 5516, 5566, 5634, 5958, 6066, 6282

Offset: 1

Muniru A Asiru, Nov 15 2017

nonn

			For m = 100, the 16 groups are C25 : C4, C100, C25 : C4, D100, C50 x C2, C5 x (C5 : C4), (C5 x C5) : C4, C20 x C5, C5 x (C5 : C4), (C5 x C5) : C4, (C5 x C5) : C4, (C5 x C5) : C4, D10 x D10, C10 x D10, C2 x ((C5 x C5) : C2), C10 x C10 where C, D mean Cyclic, Dihedral groups of the stated order and the symbols x and : mean direct and semidirect products respectively.

Muniru A Asiru, Table of n, a(n) for n = 1..339
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

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), this sequence (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

A295161:=Filtered([1..2015],n->NumberSmallGroups(n)=16);

Sequence is { m | A000001(m) = 16 }.

A294949 Numbers m such that there are precisely 17 groups of order m.

Original entry on oeis.org

675, 3267, 3549, 9947, 11475, 12625, 14283, 14749, 15525, 17745, 18875, 19575, 22707, 24353, 31725, 35775, 38759, 39039, 39825, 41209, 43561, 45387, 49735

Offset: 1

Muniru A Asiru, Nov 11 2017

nonn

			For m = 675, the 17 groups are C675, C225 x C3, C25 x ((C3 x C3) : C3), C25 x (C9 : C3), (C5 x C5) : C27, C135 x C5, C75 x C3 x C3, C9 x ((C5 x C5) : C3), (C45 x C5) : C3, C3 x ((C5 x C5) : C9), ((C5 x C5) : C9) : C3, (C15 x C15) : C3, C45 x C15, C5 x C5 x ((C3 x C3) : C3), C5 x C5 x (C9 : C3), C3 x C3 x ((C5 x C5) : C3), C15 x C15 x C3 where C means Cyclic group and the symbols x and : mean direct and semidirect products respectively.

Table of n, a(n) for n = 1..23
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

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), this sequence (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

with(GroupTheory): select(n->NumGroups(n)=17, [$1..150001]); # Muniru A Asiru, Mar 27 2018

Sequence is { m | A000001(m) = 17 }.

More terms from Muniru A Asiru, Nov 17 2017

Incorrect terms removed by Andrew Howroyd, Jan 28 2022

A298909 Numbers m such that there are precisely 18 groups of order m.

Original entry on oeis.org

156, 342, 444, 666, 732, 876, 930, 1164, 1308, 1314, 1830, 1884, 1962, 2172, 2286, 2316, 2748, 2892, 2934, 3258, 3324, 3582, 3675, 3756, 4044, 4125, 4188, 4422, 4476, 4530, 4764, 4878, 4908, 4970, 5050, 5052, 5196, 5430, 5445, 5481, 5484, 5526, 6330, 6492, 6822, 6924

Offset: 1

Muniru A Asiru, Jan 28 2018

nonn

			For m = 156, the 18 groups are (C13 : C4) : C3, C4 x (C13 : C3), C13 x (C3 : C4), C3 x (C13 : C4), C39 : C4, C156, (C13 : C4) : C3, C2 x ((C13 : C3) : C2), C3 x (C13 : C4), C39 : C4, S3 x D26, C2 x C2 x (C13 : C3), C13 x A4, (C26 x C2) : C3, C6 x D26, C26 x S3, D156, C78 x C2 where C, D mean Cyclic, Dihedral groups of the stated order and S, A mean the Symmetric, Alternating groups of the stated degree. The symbols x and : mean direct and semidirect products respectively.

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..283
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

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), this sequence (k=18), A298910 (k=19), A298911 (k=20).

Filtered([1..2015], n -> NumberSmallGroups(n) = 18);

with(GroupTheory):
for n from 1 to 10^4 do if NumGroups(n) = 18 then print(n); fi; od;

Sequence is { m | A000001(m) = 18 }.

A298911 Numbers m such that there are precisely 20 groups of order m.

Original entry on oeis.org

820, 1220, 1530, 2020, 2070, 2610, 2756, 3366, 3620, 4230, 4550, 4770, 4820, 5310, 5620, 5742, 5950, 6370, 6650, 7038, 7470, 8010, 8020, 8050, 8118, 8164, 8330, 8420, 8874, 9220, 9306, 9310, 9316, 9630, 10170, 10420, 10494, 10820, 11050

Offset: 1

Muniru A Asiru, Jan 28 2018

nonn

			For m = 820, the 20 groups are (C41 : C5) : C4, C4 x (C41 : C5), C41 x (C5 : C4), C5 x (C41 : C4), C205 : C4, C820, (C41 : C5) : C4, C2 x ((C41 : C5) : C2), C2 x C2 x (C41 : C5), C5 x (C41 : C4), C41 x (C5 : C4), C205 : C4, C205 : C4, C205 : C4, C205 : C4, D10 x D82, C10 x D82, C82 x D10, D820, C410 x C2 where C, D mean the Cyclic, Dihedral groups of the stated order and the symbols x and : mean direct and semidirect products respectively.

Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..237
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

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), A298910 (k=19), this sequence (k=20).

with(GroupTheory):
for n from 1 to 10^4 do if NumGroups(n) = 20 then print(n); fi; od;

Sequence is { m | A000001(m) = 20 }.

A056866 Orders of non-solvable groups, i.e., numbers that are not solvable numbers.

Original entry on oeis.org

60, 120, 168, 180, 240, 300, 336, 360, 420, 480, 504, 540, 600, 660, 672, 720, 780, 840, 900, 960, 1008, 1020, 1080, 1092, 1140, 1176, 1200, 1260, 1320, 1344, 1380, 1440, 1500, 1512, 1560, 1620, 1680, 1740, 1800, 1848, 1860, 1920, 1980, 2016, 2040

Offset: 1

N. J. A. Sloane, Sep 02 2000

A number is solvable if every group of that order is solvable.
This comment is about the three sequences A001034, A060793, A056866: The Feit-Thompson theorem says that a finite group with odd order is solvable, hence all numbers in this sequence are even. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 08 2001 [Corrected by Isaac Saffold, Aug 09 2021]
Insoluble group orders can be derived from A001034 (simple non-cyclic orders): k is an insoluble order iff k is a multiple of a simple non-cyclic order. - Des MacHale
All terms are divisible by 4 and either 3 or 5. - Charles R Greathouse IV, Sep 11 2012
Subsequence of A056868 and hence of A060652. - Charles R Greathouse IV, Apr 16 2015, updated Sep 11 2015
The primitive elements are A257146. Since the sum of the reciprocals of the terms of that sequence converges, this sequence has a natural density and so a(n) ~ k*n for some k (see, e.g., Erdős 1948). - Charles R Greathouse IV, Apr 17 2015
From Jianing Song, Apr 04 2022: (Start)
Burnside's p^a*q^b theorem says that a finite group whose order has at most 2 distinct prime factors is solvable, hence all terms have at least 3 distinct prime factors.
Terms not divisible by 12 are divisible by 320 and have at least 4 distinct prime factors (cf. A257391). (End)

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 2240 terms from T. D. Noe)
R. Brauer, Investigation on groups of even order, I.
R. Brauer, Investigation on groups of even order, II.
P. Erdős, On the density of some sequences of integers, Bull. Amer. Math. Soc. 54 (1948), pp. 685-692. See p. 685.
W. Feit and J. G. Thompson, A solvability criterion for finite groups and consequences, Proc. N. A. S. 48 (6) (1962) 968.
J. Pakianathan and K. Shankar, Nilpotent numbers, Amer. Math. Monthly, 107, August-September 2000, 631-634.
Cindy Tsang, Qin Chao, On the solvability of regular subgroups in the holomorph of a finite solvable group, arXiv:1901.10636 [math.GR], 2019.
Index entries for sequences related to groups

Subsequence of A000977 and A056868.

Cf. A003277, A051532, A056867, A001034, A060652.

ma[n_] := For[k = 1, True, k++, p = Prime[k]; m = 2^p*(2^(2*p) - 1); If[m > n, Return[False], If[Mod[n, m] == 0, Return[True]]]]; mb[n_] := For[k = 2, True, k++, p = Prime[k]; m = 3^p*((3^(2*p) - 1)/2); If[m > n, Return[False], If[Mod[n, m] == 0, Return[True]]]]; mc[n_] := For[k = 3, True, k++, p = Prime[k]; m = p*((p^2 - 1)/2); If[Mod[p^2 + 1, 5] == 0, If[m > n, Return[False], If[Mod[n, m] == 0, Return[True]]]]]; md[n_] := Mod[n, 2^4*3^3*13] == 0; me[n_] := For[k = 2, True, k++, p = Prime[k]; m = 2^(2*p)*(2^(2*p) + 1)*(2^p - 1); If[m > n, Return[False], If[Mod[n, m] == 0, Return[True]]]]; notSolvableQ[n_] := OddQ[n] || ma[n] || mb[n] || mc[n] || md[n] || me[n]; Select[ Range[3000], notSolvableQ] (* Jean-François Alcover, Jun 14 2012, from formula *)

is(n)={
    if(n%5616==0,return(1));
    forprime(p=2,valuation(n,2),
        if(n%(4^p-1)==0, return(1))
    );
    forprime(p=3,valuation(n,3),
        if(n%(9^p\2)==0, return(1))
    );
    forprime(p=3,valuation(n,2)\2,
        if(n%((4^p+1)*(2^p-1))==0, return(1))
    );
    my(f=factor(n)[,1]);
    for(i=1,#f,
        if(f[i]>3 && f[i]%5>1 && f[i]%5<4 && n%(f[i]^2\2)==0, return(1))
    );
    0
}; \\ Charles R Greathouse IV, Sep 11 2012

A positive integer k is a non-solvable number if and only if it is a multiple of any of the following numbers: a) 2^p*(2^(2*p)-1), p any prime. b) 3^p*(3^(2*p)-1)/2, p odd prime. c) p*(p^2-1)/2, p prime greater than 3 such that p^2 + 1 == 0 (mod 5). d) 2^4*3^3*13. e) 2^(2*p)*(2^(2*p)+1)*(2^p-1), p odd prime.

More terms from Des MacHale, Feb 19 2001

Further terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001

cp's OEIS Frontend

A249555 Numbers m such that there are precisely 12 groups of order m.

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A292896 Numbers m such that there are precisely 13 groups of order m.

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A249550 Numbers m such that there are precisely 7 groups of order m.

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A294155 Numbers m such that there are precisely 14 groups of order m.

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GAP

A294156 Numbers m such that there are precisely 15 groups of order m.

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GAP

Mathematica

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A295161 Numbers m such that there are precisely 16 groups of order m.

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GAP

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A294949 Numbers m such that there are precisely 17 groups of order m.

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Maple

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A298909 Numbers m such that there are precisely 18 groups of order m.

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