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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. 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 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.)