cp's OEIS Frontend

A046055 Orders of finite Abelian groups having the incrementally largest numbers of nonisomorphic forms (A046054).

%I A046055 #53 Feb 16 2025 08:32:38
%S A046055 1,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T A046055 131072,221184,262144,442368,524288,663552,884736,995328,1048576,
%U A046055 1327104,1769472,1990656,2097152,2654208,3538944,3981312,4194304
%N A046055 Orders of finite Abelian groups having the incrementally largest numbers of nonisomorphic forms (A046054).
%C A046055 Different from A151821, but often confused with it.
%C A046055 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 A046055 Amiram Eldar, <a href="/A046055/b046055.txt">Table of n, a(n) for n = 1..1111</a> (terms 1..216 from Charlie Neder)
%H A046055 H. D. Nguyen, D. Taggart, <a href="https://citeseerx.ist.psu.edu/pdf/8f2f36f22878c984775ed04368b8893879b99458">Mining the OEIS: Ten Experimental Conjectures</a>, 2013. Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
%H A046055 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 A046055 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AbelianGroup.html">Abelian Group.</a>
%H A046055 Wikipedia, <a href="http://en.wikipedia.org/wiki/Abelian_group">Abelian group</a>
%H A046055 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A046055 Warning: the g.f. is not x*(1+2*x)/(1-2*x), as claimed earlier.
%F A046055 Warning: this is not the binomial transform of A010684, as claimed earlier.
%F A046055 Warning: this is not the row sums of either A131127 or A134058, as claimed earlier.
%t A046055 aa = {}; max = 0; Do[If[FiniteAbelianGroupCount[n] > max, max = FiniteAbelianGroupCount[n]; AppendTo[aa, n]], {n, 2^22}]; aa (* _Artur Jasinski_, Oct 06 2011 *)
%Y A046055 Cf. A000079, A000688, A046054, A046056, A010684.
%Y A046055 Warning: this is different from A151821.
%K A046055 nonn,nice
%O A046055 1,2
%A A046055 _Eric W. Weisstein_
%E A046055 More terms from _David Wasserman_, Feb 06 2002
%E A046055 Many incorrect formulas and assertions deleted by _R. J. Mathar_, Jul 08 2009
%E A046055 Edited by _N. J. A. Sloane_, Jul 08 2009