A051881 Number of subgroups of order n in special orthogonal group SO(3).
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, 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, 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
Offset: 1
Examples
The groups are "nn", of order n; "22n", of order 2n; "332", "432", "532" of orders 12,24,60.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..12000
Crossrefs
Programs
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Mathematica
a[2] = 1; a[12|24|60] = 3; a[n_] := 2-Mod[n, 2]; Array[a, 105] (* Jean-François Alcover, Nov 12 2015 *)
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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
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Python
def a(n): if n == 2: return 1 elif n in {12, 24, 60}: return 3 else: return 2 - n % 2 # Paul Muljadi, Oct 21 2024
Formula
Has period 1, 2 except for a(2) = 1, a(12) = a(24) = a(60) = 3.
Extensions
More terms from James Sellers and David W. Wilson, Dec 16 1999