A324842 Matula-Goebel numbers of rooted trees where the branches of any branch of any terminal subtree form a submultiset of the branches of the same subtree.

1, 2, 4, 6, 8, 12, 16, 18, 24, 28, 32, 36, 48, 54, 56, 64, 72, 78, 84, 96, 108, 112, 128, 144, 152, 156, 162, 168, 192, 196, 216, 224, 234, 252, 256, 288, 304, 312, 324, 336, 384, 392, 432, 444, 448, 456, 468, 486, 504, 512, 576, 588, 608, 624, 648, 672, 702

Offset

1,2

Links

Table of n, a(n) for n=1..57.

Example

The sequence of rooted trees together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   4: (oo)
   6: (o(o))
   8: (ooo)
  12: (oo(o))
  16: (oooo)
  18: (o(o)(o))
  24: (ooo(o))
  28: (oo(oo))
  32: (ooooo)
  36: (oo(o)(o))
  48: (oooo(o))
  54: (o(o)(o)(o))
  56: (ooo(oo))
  64: (oooooo)
  72: (ooo(o)(o))
  78: (o(o)(o(o)))
  84: (oo(o)(oo))
  96: (ooooo(o))

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
qaQ[n_]:=And[And@@Table[Divisible[n, x], {x, primeMS[n]}], And@@qaQ/@primeMS[n]];
Select[Range[1000], qaQ]

Crossrefs

A subsequence of A120383.

Cf. A000081, A007097, A112798, A279861, A290689, A290760, A290822, A318186.

Cf. A324704, A324736, A324748, A324753, A324843, A324847, A324848, A324854.

Sequence in context: A128397 A377385 A120383 * A055932 A140067 A364157

Adjacent sequences: A324839 A324840 A324841 * A324843 A324844 A324845

Keyword

nonn

Author

Gus Wiseman, Mar 18 2019

Status

approved