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%I #24 Mar 20 2020 10:41:51
%S 1,1,2,4,8,13,21,31,49,74,113,139,216,268
%N Number of distinct orders of subgroups of the symmetric group.
%H L. Naughton and G. Pfeiffer, <a href="http://arxiv.org/abs/1211.1911">Integer sequences realized by the subgroup pattern of the symmetric group</a>, arXiv:1211.1911 [math.GR], 2012-2013 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Naughton/naughton2.html">J. Int. Seq. 16 (2013) #13.5.8</a>
%H Liam Naughton, <a href="http://www.maths.nuigalway.ie/~liam/CountingSubgroups.g">CountingSubgroups.g</a>
%H Liam Naughton and Goetz Pfeiffer, <a href="http://schmidt.nuigalway.ie/tomlib/">Tomlib, The GAP table of marks library</a>,
%o (GAP)
%o Size(DuplicateFreeList(List(ConjugacyClassesSubgroups(G), x-> Size(Representative (x)))));
%o (Sage)
%o def A218913(n):
%o G = SymmetricGroup(n)
%o subgroups = G.conjugacy_classes_subgroups()
%o return len(set(subG.cardinality() for subG in subgroups))
%o # _Peter Luschny_, Apr 21 2016
%K nonn,more
%O 0,3
%A _Liam Naughton_, Nov 09 2012
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