

A046055


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


19



1, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 221184, 262144, 442368, 524288, 663552, 884736, 995328, 1048576, 1327104, 1769472, 1990656, 2097152, 2654208, 3538944, 3981312, 4194304
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Different from A151821, but often confused with it.
Nicolas used the notation a(n) for the number of Abelian groups of order n (A000688) and named these numbers ahighly composite numbers (ahautement composés).  Amiram Eldar, Aug 20 2019


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1111 (terms 1..216 from Charlie Neder)
H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013. Mentions this sequence.  From N. J. A. Sloane, Mar 16 2014
JeanLouis Nicolas, Sur les entiers N pour lesquels il y a beaucoup de groupes abéliens d’ordre N, Annales de l'institut Fourier. Vol. 28, No. 4. (1978), pp. 116, alternative link.
Eric Weisstein's World of Mathematics, Abelian Group.
Wikipedia, Abelian group
Index entries for sequences related to enumerating groups.


FORMULA

Warning: the g.f. is not x*(1+2*x)/(12*x), as claimed earlier.
Warning: this is not the binomial transform of A010684, as claimed earlier.
Warning: this is not the row sums of either A131127 or A134058, as claimed earlier.


MATHEMATICA

aa = {}; max = 0; Do[If[FiniteAbelianGroupCount[n] > max, max = FiniteAbelianGroupCount[n]; AppendTo[aa, n]], {n, 2^22}]; aa (* Artur Jasinski, Oct 06 2011 *)


CROSSREFS

Cf. A000079, A000688, A046054, A046056, A010684.
Warning: this is different from A151821.
Sequence in context: A307870 A330873 A233442 * A186949 A020707 A151821
Adjacent sequences: A046052 A046053 A046054 * A046056 A046057 A046058


KEYWORD

nonn,nice


AUTHOR

Eric W. Weisstein


EXTENSIONS

More terms from David Wasserman, Feb 06 2002
Many incorrect formulas and assertions deleted by R. J. Mathar, Jul 08 2009
Edited by N. J. A. Sloane, Jul 08 2009


STATUS

approved



