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A218913
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Number of distinct orders of subgroups of the symmetric group.
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4
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1, 1, 2, 4, 8, 13, 21, 31, 49, 74, 113, 139, 216, 268
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..13.
L. Naughton and G. Pfeiffer, Integer sequences realized by the subgroup pattern of the symmetric group, arXiv:1211.1911 [math.GR], 2012-2013 and J. Int. Seq. 16 (2013) #13.5.8
Liam Naughton, CountingSubgroups.g
Liam Naughton and Goetz Pfeiffer, Tomlib, The GAP table of marks library,
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PROG
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(GAP)
Size(DuplicateFreeList(List(ConjugacyClassesSubgroups(G), x-> Size(Representative (x)))));
(Sage)
def A218913(n):
G = SymmetricGroup(n)
subgroups = G.conjugacy_classes_subgroups()
return len(set(subG.cardinality() for subG in subgroups))
# Peter Luschny, Apr 21 2016
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CROSSREFS
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Sequence in context: A005282 A046185 A259964 * A349061 A241691 A164429
Adjacent sequences: A218910 A218911 A218912 * A218914 A218915 A218916
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KEYWORD
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nonn,more
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AUTHOR
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Liam Naughton, Nov 09 2012
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STATUS
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approved
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