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.

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

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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.
		

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 }.