A303024 Matula-Goebel numbers of anti-binary (no binary branchings) rooted trees.

1, 2, 3, 5, 8, 11, 12, 16, 18, 19, 20, 24, 27, 30, 31, 32, 36, 37, 40, 44, 45, 48, 50, 53, 54, 60, 61, 64, 66, 67, 71, 72, 75, 76, 80, 81, 88, 89, 90, 96, 99, 100, 103, 108, 110, 113, 114, 120, 124, 125, 127, 128, 131, 132, 135, 144, 148, 150, 151, 152, 157

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Example

The sequence of anti-binary rooted trees together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   5: (((o)))
   8: (ooo)
  11: ((((o))))
  12: (oo(o))
  16: (oooo)
  18: (o(o)(o))
  19: ((ooo))
  20: (oo((o)))
  24: (ooo(o))
  27: ((o)(o)(o))
  30: (o(o)((o)))
  31: (((((o)))))

Mathematica

abQ[n_]:=Or[n==1, And[PrimeOmega[n]!=2, And@@Cases[FactorInteger[n], {p_, _}:>abQ[PrimePi[p]]]]]
Select[Range[100], abQ]

Crossrefs

Cf. A000081, A000598, A001190, A001678, A007097, A061775, A111299, A292050, A298422, A298424.

Cf. A303022, A303023, A303025, A303026, A303027.

Sequence in context: A189716 A002480 A173672 * A070223 A298120 A298205

Adjacent sequences: A303021 A303022 A303023 * A303025 A303026 A303027

Keyword

nonn

Author

Gus Wiseman, Aug 15 2018

Status

approved