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

1,5

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

Formula

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

Crossrefs

Cf. A181771, A181769, A196111.

Sequence in context: A187886 A324103 A130054 * A196111 A261628 A007431

Adjacent sequences: A236143 A236144 A236145 * A236147 A236148 A236149

Keyword

nonn,hard,more

Author

James McCarron, Feb 03 2014

Status

approved