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

Author

Gus Wiseman, Jul 04 2018

Keywords

• nonn

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.

Examples

			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))
		

Crossrefs

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

Programs

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[#]]]&]