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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 a-highly composite numbers (a-hautement 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

Jean-Louis 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. 1-16, 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)/(1-2*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

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Last modified August 5 15:48 EDT 2020. Contains 336213 sequences. (Running on oeis4.)