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%I #31 Dec 12 2023 07:48:42
%S 32,48,64,96,128,144,160,192,256,288,320,384,432,448,480,512,576,640,
%T 648,672,704,720,768,800,832,864,896,960,1024,1088,1152,1216,1248,
%U 1280,1296,1344,1408,1440,1458,1536,1600,1664,1728,1792,1920,1944,2016,2048,2112,2160,2176,2187,2240,2304,2400,2432,2496,2560,2592,2688,2816,2880,2916,2944
%N Group-abundant numbers: n such that the number of groups of order n (A000001) exceeds n.
%C It seems fairly certain that 1 is the only group-perfect number and that almost all numbers are group-deficient. However, all that is known at present is that all squarefree numbers except 1 are group-deficient.
%H Alex Meiburg, <a href="/A090052/b090052.txt">Table of n, a(n) for n = 1..178</a>
%H J. H. Conway, Heiko Dietrich and E. A. O'Brien, <a href="http://www.math.auckland.ac.nz/~obrien/research/gnu.pdf">Counting groups: gnus, moas and other exotica</a>.
%e 32 is in the sequence because A000001(32) = 51 > 32, 48 is in the sequence because A000001(48) = 52 > 48 and since the exact number of groups of order 2048 that have exponent-2 class 2 is 1774274116992170 then 2048 is in the sequence because A000001(2048) > 1774274116992170 > 2048. - _Muniru A Asiru_, Nov 26 2017
%o (GAP) A090052 := Filtered([1..2015], n -> NumberSmallGroups(n) > n); # _Muniru A Asiru_, Nov 30 2017
%Y Cf. A000001.
%K nonn
%O 1,1
%A _J. H. Conway_, Jan 21 2004
%E 1944, 2016, and 2048 added by _Eric M. Schmidt_, Aug 02 2012
%E a(49)-a(52) from _Muniru A Asiru_, Nov 26 2017
%E a(53)-a(178) from _Alex Meiburg_, Dec 30 2017, partially using https://github.com/olexandr-konovalov/gnu/
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