

A090052


Groupabundant numbers: n such that the number of groups of order n (A000001) exceeds n.


2



32, 48, 64, 96, 128, 144, 160, 192, 256, 288, 320, 384, 432, 448, 480, 512, 576, 640, 648, 672, 704, 720, 768, 800, 832, 864, 896, 960, 1024, 1088, 1152, 1216, 1248, 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
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OFFSET

1,1


COMMENTS

It seems fairly certain that 1 is the only groupperfect number and that almost all numbers are groupdeficient. However, all that is known at present is that all squarefree numbers except 1 are groupdeficient.


LINKS



EXAMPLE

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 exponent2 class 2 is 1774274116992170 then 2048 is in the sequence because A000001(2048) > 1774274116992170 > 2048.  Muniru A Asiru, Nov 26 2017


PROG



CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

a(53)a(178) from Alex Meiburg, Dec 30 2017, partially using https://github.com/olexandrkonovalov/gnu/


STATUS

approved



