A324766 Matula-Goebel numbers of recursively anti-transitive rooted trees.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 31, 32, 33, 34, 35, 40, 44, 46, 49, 50, 51, 53, 57, 59, 62, 63, 64, 67, 68, 71, 73, 77, 79, 80, 81, 83, 85, 87, 88, 92, 93, 95, 97, 99, 100, 103, 109, 115, 118, 121, 124, 125, 127, 128

Offset

1,2

Comments

The complement is {6, 12, 13, 14, 15, 18, 24, 26, 28, 30, 36, ...}.

An unlabeled rooted tree is recursively anti-transitive if no branch of a branch of a terminal subtree is a branch of the same subtree.

Links

Table of n, a(n) for n=1..64.

Example

The sequence of 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))
  10: (o((o)))
  11: ((((o))))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  20: (oo((o)))
  21: ((o)(oo))
  22: (o(((o))))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))
  29: ((o((o))))
  31: (((((o)))))
  32: (ooooo)
  33: ((o)(((o))))
  34: (o((oo)))
  35: (((o))(oo))
  40: (ooo((o)))
  44: (oo(((o))))
  46: (o((o)(o)))
  49: ((oo)(oo))
  50: (o((o))((o)))

Mathematica

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

Crossrefs

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

Cf. A324695, A324751, A324756, A324758, A324765, A324767, A324769, A324838, A324841, A324844.

Sequence in context: A114994 A357006 A137706 * A336621 A039224 A161508

Adjacent sequences: A324763 A324764 A324765 * A324767 A324768 A324769

Keyword

nonn

Author

Gus Wiseman, Mar 17 2019

Status

approved