A316470 Matula-Goebel numbers of unlabeled rooted RPMG-trees, meaning the Matula-Goebel numbers of the branches of any non-leaf node are relatively prime.

1, 2, 4, 6, 8, 12, 14, 16, 18, 24, 26, 28, 32, 36, 38, 42, 48, 52, 54, 56, 64, 72, 74, 76, 78, 84, 86, 96, 98, 104, 106, 108, 112, 114, 122, 126, 128, 144, 148, 152, 156, 162, 168, 172, 178, 182, 192, 196, 202, 208, 212, 214, 216, 222, 224, 228, 234, 244, 252

Offset

1,2

Comments

A prime index of n is a number m such that prime(m) divides n. A number is in the sequence iff it is 1 or its prime indices are relatively prime and already belong to the sequence.

Links

Table of n, a(n) for n=1..59.

Example

The sequence of all RPMG-trees preceded by their Matula-Goebel numbers begins:
   1: o
   2: (o)
   4: (oo)
   6: (o(o))
   8: (ooo)
  12: (oo(o))
  14: (o(oo))
  16: (oooo)
  18: (o(o)(o))
  24: (ooo(o))
  26: (o(o(o)))
  28: (oo(oo))
  32: (ooooo)
  36: (oo(o)(o))
  38: (o(ooo))
  42: (o(o)(oo))

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Or[#==1, And[GCD@@primeMS[#]==1, And@@#0/@primeMS[#]]]&]

Crossrefs

Cf. A000081, A000837, A007097, A289509, A302796, A316468, A316469, A316473, A316475, A316495.

Sequence in context: A254748 A217562 A088879 * A290822 A318186 A139363

Adjacent sequences: A316467 A316468 A316469 * A316471 A316472 A316473

Keyword

nonn

Author

Gus Wiseman, Jul 04 2018

Status

approved