A126102 Number of pointed groups of order n: that is, Sum_{G = group of order n} Number of conjugacy classes in G.

1, 2, 3, 8, 5, 9, 7, 34, 18, 14, 11, 40, 13, 19, 15, 161, 17, 57, 19, 61, 26, 29, 23, 197, 50, 34, 103, 76, 29, 66, 31, 912, 33, 44, 35, 267, 37, 49, 46, 293, 41, 107, 43, 116, 90, 59, 47, 1096, 98, 148, 51, 143, 53, 371, 62, 377, 66, 74, 59, 325, 61, 79, 156, 7068

Offset

1,2

Comments

Number of pairs (G, g in G) for G a group of order n.

This has the same relation to A000001 (groups) as A000081 (pointed trees, also called rooted trees) does to trees (A000055).

Links

Klaus Brockhaus, Table of n, a(n) for n=1..255

Prog

(Magma) SmallGroupDatabase();
for o in [1..64] do
t1:=0;
t2:=NumberOfSmallGroups(o);
for n in [1..t2] do
G:=Group(o, n);
t1:=t1 + #ConjugacyClasses(G);
end for;
print(t1);
end for;
(Magma) D:=SmallGroupDatabase(); [ &+[ #ConjugacyClasses(Group(D, o, n)): n in [1..NumberOfSmallGroups(D, o)] ]: o in [1..64] ]; /* Klaus Brockhaus, Mar 06 2007 */

Crossrefs

Cf. A000001 (groups). See A126103 for a different and better version.

Sequence in context: A154760 A231817 A114340 * A011433 A349824 A332221

Adjacent sequences: A126099 A126100 A126101 * A126103 A126104 A126105

Keyword

nonn

Author

N. J. A. Sloane, Mar 06 2007

Status

approved