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%I #50 Jun 22 2021 02:57:41
%S 1,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T 131072,221184,262144,442368,524288,663552,884736,995328,1048576,
%U 1327104,1769472,1990656,2097152,2654208,3538944,3981312,4194304
%N Orders of finite Abelian groups having the incrementally largest numbers of nonisomorphic forms (A046054).
%C Different from A151821, but often confused with it.
%C Nicolas used the notation a(n) for the number of Abelian groups of order n (A000688) and named these numbers a-highly composite numbers (a-hautement composés). - _Amiram Eldar_, Aug 20 2019
%H Amiram Eldar, <a href="/A046055/b046055.txt">Table of n, a(n) for n = 1..1111</a> (terms 1..216 from Charlie Neder)
%H H. D. Nguyen, D. Taggart, <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.391.2522&rep=rep1&type=pdf">Mining the OEIS: Ten Experimental Conjectures</a>, 2013. Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
%H Jean-Louis Nicolas, <a href="https://doi.org/10.5802/aif.714">Sur les entiers N pour lesquels il y a beaucoup de groupes abéliens d’ordre N</a>, Annales de l'institut Fourier. Vol. 28, No. 4. (1978), pp. 1-16, <a href="http://www.numdam.org/item/AIF_1978__28_4_1_0">alternative link</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AbelianGroup.html">Abelian Group.</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Abelian_group">Abelian group</a>
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F Warning: the g.f. is not x*(1+2*x)/(1-2*x), as claimed earlier.
%F Warning: this is not the binomial transform of A010684, as claimed earlier.
%F Warning: this is not the row sums of either A131127 or A134058, as claimed earlier.
%t aa = {}; max = 0; Do[If[FiniteAbelianGroupCount[n] > max, max = FiniteAbelianGroupCount[n]; AppendTo[aa, n]], {n, 2^22}]; aa (* _Artur Jasinski_, Oct 06 2011 *)
%Y Cf. A000079, A000688, A046054, A046056, A010684.
%Y Warning: this is different from A151821.
%K nonn,nice
%O 1,2
%A _Eric W. Weisstein_
%E More terms from _David Wasserman_, Feb 06 2002
%E Many incorrect formulas and assertions deleted by _R. J. Mathar_, Jul 08 2009
%E Edited by _N. J. A. Sloane_, Jul 08 2009
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