A384727 Number of groups of order n (up to isomorphism) with exactly n subgroups.

1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1

Offset: 1

Author

Richard Stanley, Jun 08 2025

Keywords

• nonn

Comments

See A384800 for more information.

Examples

			The symmetric group S_3 has six elements and six subgroups. The other group of order six has four subgroups, so a(6)=1.
		

Links

• Richard Stanley, Table of n, a(n) for n = 1..192
• Richard Stanley, What finite groups have as many elements as subgroups? Question in Mathoverflow, answered by Dave Benson and others, Jun 07 2025.

Crossrefs

Cf. A368538, A384800.