cp's OEIS Frontend

A324769 Matula-Goebel numbers of fully anti-transitive rooted trees.

%I A324769 #4 Mar 18 2019 08:15:37
%S A324769 1,2,3,4,5,7,8,9,11,13,16,17,19,21,23,25,27,29,31,32,35,37,41,43,47,
%T A324769 49,51,53,57,59,61,63,64,65,67,71,73,77,79,81,83,85,89,91,95,97,101,
%U A324769 103,107,109,113,115,121,125,127,128,129,131,133,137,139,143,147
%N A324769 Matula-Goebel numbers of fully anti-transitive rooted trees.
%C A324769 An unlabeled rooted tree is fully anti-transitive if no proper terminal subtree of any branch of the root is a branch of the root.
%e A324769 The sequence of fully anti-transitive rooted trees together with their Matula-Goebel numbers begins:
%e A324769    1: o
%e A324769    2: (o)
%e A324769    3: ((o))
%e A324769    4: (oo)
%e A324769    5: (((o)))
%e A324769    7: ((oo))
%e A324769    8: (ooo)
%e A324769    9: ((o)(o))
%e A324769   11: ((((o))))
%e A324769   13: ((o(o)))
%e A324769   16: (oooo)
%e A324769   17: (((oo)))
%e A324769   19: ((ooo))
%e A324769   21: ((o)(oo))
%e A324769   23: (((o)(o)))
%e A324769   25: (((o))((o)))
%e A324769   27: ((o)(o)(o))
%e A324769   29: ((o((o))))
%e A324769   31: (((((o)))))
%e A324769   32: (ooooo)
%e A324769   35: (((o))(oo))
%e A324769   37: ((oo(o)))
%e A324769   41: (((o(o))))
%e A324769   43: ((o(oo)))
%e A324769   47: (((o)((o))))
%e A324769   49: ((oo)(oo))
%t A324769 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A324769 fullantiQ[n_]:=Intersection[Union@@Rest[FixedPointList[Union@@primeMS/@#&,primeMS[n]]],primeMS[n]]=={};
%t A324769 Select[Range[100],fullantiQ]
%Y A324769 Cf. A000081, A007097, A276625, A290760, A304360, A306844.
%Y A324769 Cf. A324695, A324751, A324756, A324758, A324766, A324768, A324770.
%Y A324769 Cf. A324838, A324841, A324845, A324846.
%K A324769 nonn
%O A324769 1,2
%A A324769 _Gus Wiseman_, Mar 17 2019