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%I #17 Oct 01 2018 03:33:47
%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
%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
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