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A090052 Group-abundant 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Alex Meiburg, Table of n, a(n) for n = 1..178

J. H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica.

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

PROG

(GAP) A090052 := Filtered([1..2015], n -> NumberSmallGroups(n) > n); # Muniru A Asiru, Nov 30 2017

CROSSREFS

Cf. A000001.

Sequence in context: A114416 A046304 A114447 * A163285 A036329 A014614

Adjacent sequences:  A090049 A090050 A090051 * A090053 A090054 A090055

KEYWORD

nonn

AUTHOR

J. H. Conway, Jan 21 2004

EXTENSIONS

1944, 2016, and 2048 added by Eric M. Schmidt, Aug 02 2012

a(49)-a(52) from Muniru A Asiru, Nov 26 2017

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

STATUS

approved

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Last modified October 18 05:45 EDT 2019. Contains 328146 sequences. (Running on oeis4.)