A046056 - OEIS

A046056

Smallest order for which there are n nonisomorphic finite Abelian groups, or 0 if no such order exists.

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

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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 groups

CROSSREFS