cp's OEIS Frontend

A051881 Number of subgroups of order n in special orthogonal group SO(3).

%I A051881 #25 Jul 02 2025 16:01:58
%S A051881 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 A051881 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 A051881 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 A051881 Number of subgroups of order n in special orthogonal group SO(3).
%H A051881 Antti Karttunen, <a href="/A051881/b051881.txt">Table of n, a(n) for n = 1..12000</a>
%F A051881 Has period 1, 2 except for a(2) = 1, a(12) = a(24) = a(60) = 3.
%e A051881 The groups are "nn", of order n; "22n", of order 2n; "332", "432", "532" of orders 12,24,60.
%t A051881 a[2] = 1; a[12|24|60] = 3; a[n_] := 2-Mod[n, 2]; Array[a, 105] (* _Jean-François Alcover_, Nov 12 2015 *)
%o A051881 (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 A051881 (Python)
%o A051881 def a(n):
%o A051881     if n == 2:
%o A051881         return 1
%o A051881     elif n in {12, 24, 60}:
%o A051881         return 3
%o A051881     else:
%o A051881         return 2 - n % 2 # _Paul Muljadi_, Oct 21 2024
%Y A051881 The main sequences concerned with group theory are A000001, A000679, A001034, A001051, A001228, A005180, A000019, A000637, A000638, A002106, A005432, A051881.
%K A051881 nonn,easy,nice
%O A051881 1,4
%A A051881 _J. H. Conway_
%E A051881 More terms from _James Sellers_ and _David W. Wilson_, Dec 16 1999