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

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, 49, 51, 53, 57, 59, 61, 63, 64, 65, 67, 71, 73, 77, 79, 81, 83, 85, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 121, 125, 127, 128, 129, 131, 133, 137, 139, 143, 147

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..63.

Example

The sequence of fully 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))))
  13: ((o(o)))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  21: ((o)(oo))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))
  29: ((o((o))))
  31: (((((o)))))
  32: (ooooo)
  35: (((o))(oo))
  37: ((oo(o)))
  41: (((o(o))))
  43: ((o(oo)))
  47: (((o)((o))))
  49: ((oo)(oo))

Mathematica

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

Crossrefs

Cf. A000081, A007097, A276625, A290760, A304360, A306844.

Cf. A324695, A324751, A324756, A324758, A324766, A324768, A324770.

Cf. A324838, A324841, A324845, A324846.

Sequence in context: A273200 A360117 A014567 * A328867 A326536 A322902

Adjacent sequences: A324766 A324767 A324768 * A324770 A324771 A324772

Keyword

nonn

Author

Gus Wiseman, Mar 17 2019

Status

approved