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A126102
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Number of pointed groups of order n: that is, Sum_{G = group of order n} Number of conjugacy classes in G.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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Klaus Brockhaus, Table of n, a(n) for n=1..255
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PROG
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(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, a more compact version) D:=SmallGroupDatabase(); [ &+[ #ConjugacyClasses(Group(D, o, n)): n in [1..NumberOfSmallGroups(D, o)] ]: o in [1..64] ]; /* Klaus Brockhaus, Mar 06 2007 */
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CROSSREFS
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Cf. A000001 (groups). See A126103 for a different and better version.
Sequence in context: A089489 A154760 A114340 * A011433 A126139 A060872
Adjacent sequences: A126099 A126100 A126101 * A126103 A126104 A126105
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Mar 06 2007
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STATUS
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approved
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