A132126 Number of nonassociative subloops of order 8n of the Cayley octonions (up to isomorphism).

0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Paul Boddington, Oct 31 2007

Keywords

• easy
• nonn

Comments

Every nonassociative subloop of the octonions has order a multiple of 8.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• P. Boddington and D. Rumynin, On Curtis' theorem about finite octonionic loops, Proc. Amer. Math. Soc. 135 (2007), 1651-1657.

Crossrefs

Cf. A090750.

Programs

Mathematica

ReplacePart[PadRight[{0},120,1],{6->2,12->2,30->3}] (* Harvey P. Dale, Dec 18 2018 *)

PARI

A132126(n) = if(1==n,0,if((6==n)||(12==n),2,if(30==n,3,1))); \\ Antti Karttunen, Sep 27 2018

Formula

a(1) = 0, a(6) = 2, a(12) = 2, a(30) = 3, otherwise a(n) = 1.