A249552 Numbers m such that there are precisely 9 groups of order m.

308, 532, 644, 836, 868, 1316, 1364, 1652, 1748, 1815, 1876, 1892, 2068, 2212, 2324, 2356, 2596, 2852, 2884, 2996, 3124, 3268, 3476, 3572, 3652, 3668, 3892, 3956, 4228, 4263, 4484, 4532, 4564, 4676, 4708, 5012, 5092, 5332, 5348, 5396, 5428, 5572, 5588, 5764, 5828, 6004, 6116, 6164, 6244, 6308, 6356, 6532

Offset: 1

Author

N. J. A. Sloane, Nov 01 2014

Keywords

• nonn

Links

• Muniru A Asiru and Jorge R. F. F. Lopes, Table of n, a(n) for n = 1..456
• Max Horn, Numbers of isomorphism types of finite groups of given order
• Index entries for sequences related to groups

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), this sequence (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

GAP

A249552:=Filtered([1..2015],n->NumberSmallGroups(n)=9); # Muniru A Asiru, Nov 17 2017

Maple

select(t -> GroupTheory:-NumAbelianGroups(t) <= 9 and GroupTheory:-NumGroups(t) = 9, [$1..10000]); # Robert Israel, Mar 26 2018

Extensions

a(13)-a(16) from Muniru A Asiru, Oct 21 2017

More terms from Muniru A Asiru, Oct 23 2017

More terms from Muniru A Asiru, Nov 17 2017

Incorrect b-file shortened by Jorge R. F. F. Lopes, Jan 07 2022