A236146 Number of primitive quandles of order n, up to isomorphism. A quandle is primitive if its inner automorphism groups acts primitively on it.

1, 0, 1, 1, 3, 0, 5, 2, 3, 1, 9, 0, 11, 1, 3, 15, 0, 17, 0, 1, 0, 21, 0, 10, 0, 8, 2, 27, 0, 29, 6, 0, 0, 0

Offset: 1

Author

James McCarron, Feb 03 2014

Keywords

• nonn
• hard
• more

Comments

Since a primitive quandle is connected, we have a(n) <= A181771(n) for all n.

Furthermore, since a primitive quandle is simple, we have a(n) <= A196111(n) for all n.

Links

• James McCarron, Table of n, a(n) for n = 1..34
• Wikipedia, Racks and quandles
• James McCarron, Connected Quandles with Order Equal to Twice an Odd Prime
• Leandro Vendramin, Doubly transitive groups and cyclic quandles

Crossrefs

Cf. A181771, A181769, A196111.

Formula

For odd primes p, a(p) = p - 2.