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Number of subgroups of order n in special orthogonal group SO(3).
2

%I #24 Nov 05 2024 20:40:00

%S 1,1,1,2,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2,1,2,

%T 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2,

%U 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1

%N Number of subgroups of order n in special orthogonal group SO(3).

%H Antti Karttunen, <a href="/A051881/b051881.txt">Table of n, a(n) for n = 1..12000</a>

%F Has period 1, 2 except for a(2) = 1, a(12) = a(24) = a(60) = 3.

%e The groups are "nn", of order n; "22n", of order 2n; "332", "432", "532" of orders 12,24,60.

%t a[2] = 1; a[12|24|60] = 3; a[n_] := 2-Mod[n, 2]; Array[a, 105] (* _Jean-François Alcover_, Nov 12 2015 *)

%o (PARI) a(n)=if(n==2||n==12||n==24||n==60, if(n>2,3,1), if(n%2,1,2)) \\ _Charles R Greathouse IV_, Nov 10 2015

%o (Python)

%o def a(n):

%o if n == 2:

%o return 1

%o elif n in {12, 24, 60}:

%o return 3

%o else:

%o return 2 - n % 2 # _Paul Muljadi_, Oct 21 2024

%Y The main sequences concerned with group theory are A000001, A000679, A001034, A001051, A001228, A005180, A000019, A000637, A000638, A002106, A005432, A051881.

%K nonn,easy,nice

%O 1,4

%A _J. H. Conway_

%E More terms from _James A. Sellers_ and _David W. Wilson_, Dec 16 1999