A303026 Matula-Goebel numbers of series-reduced anti-binary (no unary or binary branchings) rooted trees.

1, 8, 16, 32, 64, 76, 128, 152, 212, 256, 304, 424, 512, 524, 608, 722, 848, 1024, 1048, 1216, 1244, 1444, 1532, 1696, 2014, 2048, 2096, 2432, 2488, 2876, 2888, 3064, 3392, 3524, 4028, 4096, 4192, 4864, 4976, 4978, 5204, 5618, 5752, 5776, 6128, 6476, 6784

Offset

1,2

Links

Table of n, a(n) for n=1..47.

Example

The sequence of series-reduced anti-binary rooted trees together with their Matula-Goebel numbers begins:
     1: o
     8: (ooo)
    16: (oooo)
    32: (ooooo)
    64: (oooooo)
    76: (oo(ooo))
   128: (ooooooo)
   152: (ooo(ooo))
   212: (oo(oooo))
   256: (oooooooo)
   304: (oooo(ooo))
   424: (ooo(oooo))
   512: (ooooooooo)
   524: (oo(ooooo))
   608: (ooooo(ooo))
   722: (o(ooo)(ooo))
   848: (oooo(oooo))
  1024: (oooooooooo)
  1048: (ooo(ooooo))
  1216: (oooooo(ooo))
  1244: (oo(oooooo))
  1444: (oo(ooo)(ooo))
  1532: (oo(oo(ooo)))
  1696: (ooooo(oooo))
  2014: (o(ooo)(oooo))
  2048: (ooooooooooo)

Mathematica

azQ[n_]:=Or[n==1, And[PrimeOmega[n]>2, And@@Cases[FactorInteger[n], {p_, _}:>azQ[PrimePi[p]]]]]
Select[Range[1000], azQ]

Crossrefs

Cf. A000081, A000598, A001190, A001678, A007097, A061775, A102403, A111299, A292050, A298422, A298424.

Cf. A303022, A303023, A303024, A303025, A303027.

Sequence in context: A139598 A137243 A360124 * A068935 A371011 A277128

Adjacent sequences: A303023 A303024 A303025 * A303027 A303028 A303029

Keyword

nonn

Author

Gus Wiseman, Aug 15 2018

Status

approved