cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-19 of 19 results.

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

Views

Author

Muniru A Asiru, Oct 23 2017

Keywords

Examples

			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.

Links

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), 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).

Programs

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

Extensions

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

Views

Author

N. J. A. Sloane, Nov 01 2014

Keywords

Examples

			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

Links

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), 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).

Programs

  • Mathematica
    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

Formula

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

Extensions

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

Views

Author

Muniru A Asiru, Oct 24 2017

Keywords

Examples

			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.

Links

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

Programs

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

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

Views

Author

Muniru A Asiru, Nov 15 2017

Keywords

Examples

			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.

Links

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

Programs

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

Formula

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

Views

Author

Muniru A Asiru, Nov 11 2017

Keywords

Examples

			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.

Links

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

Programs

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

Formula

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

Extensions

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

Views

Author

Muniru A Asiru, Jan 28 2018

Keywords

Examples

			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.

Links

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

Programs

  • GAP
    Filtered([1..2015], n -> NumberSmallGroups(n) = 18);
  • Maple
    with(GroupTheory):
for n from 1 to 10^4 do if NumGroups(n) = 18 then print(n); fi; od;

Formula

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

Views

Author

Muniru A Asiru, Jan 28 2018

Keywords

Examples

			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.

Links

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

Programs

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

Formula

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

A298910 Numbers m such that there are precisely 19 groups of order m.

Original entry on oeis.org

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
Offset: 1

Views

Author

Muniru A Asiru, Jan 28 2018

Keywords

Examples

			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.

Links

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).

Programs

  • Maple
    with(GroupTheory):
for n from 1 to 3*10^5 do if NumGroups(n) = 19 then print(n); fi; od;

Formula

Sequence is { m | A000001(m) = 19 }.

Extensions

Shortened to remove possibly incorrect terms by Andrew Howroyd, Jan 28 2022

A295995 Numbers n such that there are precisely 15 groups of orders n and n + 1.

Original entry on oeis.org

1863, 1971, 4292, 7624, 8180, 15140, 17875, 19524, 20180, 21020, 23732, 23751, 28371, 30124, 33032, 33939, 34532, 35427, 36620, 40071, 41444, 42579, 44739, 45128, 45603, 46052
Offset: 1

Views

Author

Muniru A Asiru, Dec 02 2017

Keywords

Comments

Equivalently, lower member of consecutive terms of A294156.

Examples

			1863 is in the sequence because A000001(1863) = A000001(1864) = 15, 1971 is in the sequence because A000001(1971) = A000001(1972) = 15 and 19524 is in the sequence because A000001(19524) = A000001(19525) = 15.

Links

Crossrefs

Cf. A000001, A294156.

Formula

Sequence is { n | A000001(n) = 15, A000001(n+1) = 15 }.
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