A324841 Matula-Goebel numbers of fully recursively anti-transitive rooted trees.

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, 64, 67, 73, 77, 81, 83, 85, 95, 97, 103, 115, 121, 125, 127, 128, 131, 133, 147, 149, 153, 159, 161, 171, 175, 177, 187, 189, 201, 209, 217, 227, 233, 241, 243, 245

Offset: 1

Author

Gus Wiseman, Mar 17 2019

Keywords

• nonn

Comments

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.

Examples

			The sequence of fully recursively anti-transitive rooted trees together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   7: ((oo))
   8: (ooo)
   9: ((o)(o))
  11: ((((o))))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  21: ((o)(oo))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))
  31: (((((o)))))
  32: (ooooo)
  35: (((o))(oo))
  49: ((oo)(oo))
  51: ((o)((oo)))
  53: ((oooo))
  57: ((o)(ooo))
  59: ((((oo))))
  63: ((o)(o)(oo))
		

Crossrefs

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

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

Cf. A324838, A324840, A324844.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
fratQ[n_]:=And[Intersection[Union@@Rest[FixedPointList[Union@@primeMS/@#&,primeMS[n]]],primeMS[n]]=={},And@@fratQ/@primeMS[n]];
Select[Range[100],fratQ]