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%I #17 Jan 08 2020 17:50:45
%S 0,0,0,0,0,3,9,29,47,86,157,401,576,1316
%N Number of missing subgroup orders of the symmetric group, that is, i divides Factorial(n) but the symmetric group on n points does not have a subgroup of order i.
%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.
%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>
%F a(n) = A027423(n) - A218913(n).
%t A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A027423 = A@027423;
%t A218913 = A@218913;
%t a[n_] := A027423[[n+1]] - A218913[[n+1]];
%t a /@ Range[0, 13] (* _Jean-François Alcover_, Jan 08 2020 *)
%o (GAP) Size(Difference(DivisorsInt(Factorial(n)), DuplicateFreeList(List(ConjugacyClassesSubgroups(SymmetricGroup(n)), x->Size(Representative(x))))));
%K nonn,more
%O 0,6
%A _Liam Naughton_, Nov 09 2012
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