%I #19 Jul 17 2018 12:19:14
%S 1,1,1,4,13,31,246,1296,10774,83238,788820,6835170,81364944,848378532,
%T 11423650616,156289508025,2380629720720,33284133330760,
%U 605934954285120,9708364832948820,190330953679235040,3715069138923234960,77101583995105472880,1506549946554254503440
%N Total number of maximal cyclic subgroups of the symmetric group, counting conjugates as distinct.
%H Andrew Howroyd, <a href="/A218958/b218958.txt">Table of n, a(n) for n = 0..50</a>
%H Andrew Howroyd, <a href="/A218958/a218958.gp.txt">PARI program for this sequence and A218963</a>
%H Liam Naughton and Goetz 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>
%o (PARI) \\ See links for program script file.
%o a(n)=MaximalCyclicSubgroupCount(n, v->1); \\ _Andrew Howroyd_, Jul 17 2018
%Y Cf. A051625, A218932, A218949, A218963.
%K nonn
%O 0,4
%A _Liam Naughton_, Nov 23 2012
%E Terms a(14) and beyond from _Andrew Howroyd_, Jul 03 2018