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

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• nice

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

Cf. A000041, A000688, A033637, A046054, A046055, A046057.

Extensions

More terms from Christian G. Bower

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