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

Author

J. H. Conway

Keywords

• nonn
• easy
• nice

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

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

Programs

Mathematica

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

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

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