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A324766 Matula-Goebel numbers of recursively anti-transitive rooted trees. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A004743 A114994 A137706 * A039224 A161508 A039264

Adjacent sequences:  A324763 A324764 A324765 * A324767 A324768 A324769

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 17 2019

STATUS

approved

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Last modified April 5 03:52 EDT 2020. Contains 333238 sequences. (Running on oeis4.)