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A046056 Smallest order for which there are n nonisomorphic finite Abelian groups, or 0 if no such order exists. 9
1, 4, 8, 36, 16, 72, 32, 900, 216, 144, 64, 1800, 0, 288, 128, 44100, 0, 5400, 0, 3600, 864, 256, 0, 88200, 1296, 0, 27000, 7200, 0, 512, 0, 5336100, 1728, 0, 2592, 264600, 0, 0, 0, 176400, 0, 1024, 0, 2304, 3456, 0, 0, 10672200, 7776, 32400, 0, 0, 0, 1323000, 5184, 2048, 0, 0, 0, 4608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

There is a k: A000688(k)=n if and only if n is product of partition numbers.

LINKS

Charlie Neder, Table of n, a(n) for n = 1..1000

B. Horvat, G. Jaklic and T. Pisanski, On the number of Hamiltonian groups, arXiv:math/0503183 [math.CO], 2005.

Charlie Neder, Python program for computing this sequence

Eric Weisstein's World of Mathematics, Abelian Group.

Index entries for sequences related to enumerating groups

CROSSREFS

Cf. A000041, A000688, A046054, A046055, A046057.

Sequence in context: A149108 A149109 A266676 * A158863 A074736 A044829

Adjacent sequences:  A046053 A046054 A046055 * A046057 A046058 A046059

KEYWORD

nonn,nice

AUTHOR

Eric W. Weisstein

EXTENSIONS

More terms from Christian G. Bower

a(20) and a(28) corrected, and a(52)-a(60) from Charlie Neder, Jan 17 2019

STATUS

approved

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Last modified May 26 03:51 EDT 2019. Contains 323579 sequences. (Running on oeis4.)