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A046055 Orders of finite Abelian groups having the incrementally largest numbers of nonisomorphic forms (A046054). 18
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.

REFERENCES

H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.391.2522&rep=rep1&type=pdf. Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014

LINKS

Table of n, a(n) for n=1..33.

Eric Weisstein's World of Mathematics, Abelian Group.

Index entries for sequences related to enumerating groups.

Wikipedia, Abelian group

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 earler.

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: A005934 A085629 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 May 25 21:53 EDT 2017. Contains 287060 sequences.