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%I
%S 1,2,3,4,5,6,6,5,8,7,7,8,9,9,11,10,11,11,11,11,17,14,11,13,16,11,18,
%T 17,17,13,12,19,17,17,20,13,21,14,15,15,15,13,12,13,12,24,19,27,15,19,
%U 12,21,14,12,17,16,16,18,17,20,12,18,20,17,23,14,20,20,25
%N Number of cycles of the permutation created by length sorting on the partitions of n.
%o (PARI)
%o OrderCycs(v)={my(t=vector(#v), L=List()); for(i=1, #v, my(c=0,j=i); while(!t[j], t[j]=1; j=v[j]; c++); if(c, listput(L,c))); Vec(L)}
%o a(n)={my(u=vecsort([Vecsmall(Vecrev(p)) | p<-partitions(n)])); my(v=vecsort(u, (x,y)->lex(#x,#y), 1+4)); #OrderCycs(v)} \\ _Andrew Howroyd_, Sep 17 2019
%Y Cf. A036045-A036056.
%K nonn
%O 1,2
%A _Olivier Gérard_
%E a(31)-a(50) from _Andrew Howroyd_, Sep 17 2019
%E More terms from _Sean A. Irvine_, Oct 20 2020
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