A001051 - OEIS

%I #19 Jan 15 2019 18:42:12

%S 1,3,1,5,1,5,1,7,1,5,1,8,1,5,1,7,1,5,1,7,1,5,1,10,1,5,1,7,1,5,1,7,1,5,

%T 1,7,1,5,1,7,1,5,1,7,1,5,1,8,1,5,1,7,1,5,1,7,1,5,1,8,1,5,1,7,1,5,1,7,

%U 1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,7,1,5,1,8

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

%H Antti Karttunen, <a href="/A001051/b001051.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OrthogonalGroup.html">Orthogonal Group.</a>

%F Has period 1 5 1 7 except that a(2) = 3, a(4) = 5, a(12) = 8, a(24) = 10, a(48) = a(60) = a(120) = 8.

%t a[2] = 3; a[4] = 5; a[12] = 8; a[24] = 10; a[48] = a[60] = a[120] = 8; a[n_] := Switch[Mod[n, 4], 0, 7, 1, 1, 2, 5, 3, 1]; Table[a[n], {n, 1, 96}] (* _Jean-François Alcover_, Oct 15 2013 *)

%o (PARI) A001051(n) = if((12==n)||(48==n)||(60==n)||(120==n),8,if(24==n,10,if((4==n)||(2==n),1+n,[1,5,1,7][1+((n-1)%4)]))); \\ _Antti Karttunen_, Jan 15 2019

%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 1,2

%A _J. H. Conway_

%E Data section extended up to a(120) by _Antti Karttunen_, Jan 15 2019