A324841 - OEIS

%I #5 Mar 18 2019 08:16:02

%S 1,2,3,4,5,7,8,9,11,16,17,19,21,23,25,27,31,32,35,49,51,53,57,59,63,

%T 64,67,73,77,81,83,85,95,97,103,115,121,125,127,128,131,133,147,149,

%U 153,159,161,171,175,177,187,189,201,209,217,227,233,241,243,245

%N Matula-Goebel numbers of fully recursively anti-transitive rooted trees.

%C An unlabeled rooted tree is fully recursively anti-transitive if no proper terminal subtree of any terminal subtree is a branch of the larger subtree.

%e The sequence of fully recursively anti-transitive rooted trees together with their Matula-Goebel numbers begins:

%e    1: o

%e    2: (o)

%e    3: ((o))

%e    4: (oo)

%e    5: (((o)))

%e    7: ((oo))

%e    8: (ooo)

%e    9: ((o)(o))

%e   11: ((((o))))

%e   16: (oooo)

%e   17: (((oo)))

%e   19: ((ooo))

%e   21: ((o)(oo))

%e   23: (((o)(o)))

%e   25: (((o))((o)))

%e   27: ((o)(o)(o))

%e   31: (((((o)))))

%e   32: (ooooo)

%e   35: (((o))(oo))

%e   49: ((oo)(oo))

%e   51: ((o)((oo)))

%e   53: ((oooo))

%e   57: ((o)(ooo))

%e   59: ((((oo))))

%e   63: ((o)(o)(oo))

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t fratQ[n_]:=And[Intersection[Union@@Rest[FixedPointList[Union@@primeMS/@#&,primeMS[n]]],primeMS[n]]=={},And@@fratQ/@primeMS[n]];

%t Select[Range[100],fratQ]

%Y Cf. A000081, A007097, A290689, A303431, A304360, A306844, A316502, A318185, A318186.

%Y Cf. A324695, A324751, A324756, A324758, A324766, A324768, A324769.

%Y Cf. A324838, A324840, A324844.

%K nonn

%O 1,2

%A _Gus Wiseman_, Mar 17 2019