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A046055
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Orders of finite Abelian groups having the incrementally largest numbers of nonisomorphic forms (A046054).
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19
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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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.
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MATHEMATICA
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aa = {}; max = 0; Do[If[FiniteAbelianGroupCount[n] > max, max = FiniteAbelianGroupCount[n]; AppendTo[aa, n]], {n, 2^22}]; aa (* Artur Jasinski, Oct 06 2011 *)
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CROSSREFS
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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
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KEYWORD
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nonn,nice
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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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
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STATUS
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approved
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