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

1,6

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.

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A090750.

Sequence in context: A329801 A053255 A085856 * A324882 A345047 A031264

Adjacent sequences: A132123 A132124 A132125 * A132127 A132128 A132129

Keyword

easy,nonn

Author

Paul Boddington, Oct 31 2007

Status

approved