cp's OEIS Frontend

A218915 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.

%I A218915 #17 Jan 08 2020 17:50:45
%S A218915 0,0,0,0,0,3,9,29,47,86,157,401,576,1316
%N A218915 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 A218915 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 A218915 Liam Naughton, <a href="http://www.maths.nuigalway.ie/~liam/CountingSubgroups.g">CountingSubgroups.g</a>
%H A218915 Liam Naughton and Goetz Pfeiffer, <a href="http://schmidt.nuigalway.ie/tomlib/">Tomlib, The GAP table of marks library</a>
%F A218915 a(n) = A027423(n) - A218913(n).
%t A218915 A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {_, _}][[All, 2]]];
%t A218915 A027423 = A@027423;
%t A218915 A218913 = A@218913;
%t A218915 a[n_] := A027423[[n+1]] - A218913[[n+1]];
%t A218915 a /@ Range[0, 13] (* _Jean-François Alcover_, Jan 08 2020 *)
%o A218915 (GAP) Size(Difference(DivisorsInt(Factorial(n)), DuplicateFreeList(List(ConjugacyClassesSubgroups(SymmetricGroup(n)), x->Size(Representative(x))))));
%K A218915 nonn,more
%O A218915 0,6
%A A218915 _Liam Naughton_, Nov 09 2012