A384146 Smallest squarefree order m > 0 for which there are n nonisomorphic finite groups of order m, or 0 if no such order exists.

1, 6, 609, 30, 273, 42, 903, 510, 8729, 3255, 494711, 210, 16951, 5115, 54431, 1218

Offset: 1

Author

Robin Jones, May 21 2025

Keywords

• nonn
• more

Comments

It has been established that every n < 10000000 arises as the number of groups up to isomorphism of some squarefree m. That is, a(n) > 0 for n < 10000000.

It is conjectured that 0 never appears in this sequence.

Examples

			a(3)=609 since there are 3 groups of order 609 up to isomorphism, and 609 is the smallest squarefree integer such that there are 3 groups of that order.
		

Links

• J. H. Conway, Heiko Dietrich and E. A. O'Brien, Counting groups: gnus, moas and other exotica, Math. Intell., Vol. 30, No. 2, Spring 2008.

Crossrefs

Cf. A046057 (m not necessarily squarefree).