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

1,40

Comments

See A384800 for more information.

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.

Example

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

Crossrefs

Cf. A368538, A384800.

Sequence in context: A347706 A348381 A010103 * A086078 A353462 A323913

Adjacent sequences: A384724 A384725 A384726 * A384728 A384729 A384730

Keyword

nonn

Author

Richard Stanley, Jun 08 2025

Status

approved