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A218913 Number of distinct orders of subgroups of the symmetric group. 4
1, 1, 2, 4, 8, 13, 21, 31, 49, 74, 113, 139, 216, 268 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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,

PROG

(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

CROSSREFS

Sequence in context: A005282 A046185 A259964 * A349061 A241691 A164429

Adjacent sequences:  A218910 A218911 A218912 * A218914 A218915 A218916

KEYWORD

nonn,more

AUTHOR

Liam Naughton, Nov 09 2012

STATUS

approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)