A218913 Number of distinct orders of subgroups of the symmetric group.

1, 1, 2, 4, 8, 13, 21, 31, 49, 74, 113, 139, 216, 268

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