A316494 Matula-Goebel numbers of locally disjoint rooted identity trees, meaning no branch overlaps any other branch of the same root.

1, 2, 3, 5, 6, 10, 11, 13, 15, 22, 26, 29, 30, 31, 33, 41, 47, 55, 58, 62, 66, 79, 82, 93, 94, 101, 109, 110, 113, 123, 127, 137, 141, 143, 145, 155, 158, 165, 179, 186, 202, 205, 211, 218, 226, 246, 254, 257, 271, 274, 282, 286, 290, 293, 310, 317, 327, 330

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 either it is equal to 1, it is a prime number whose prime index already belongs to the sequence, or its prime indices are pairwise coprime, distinct, and already belong to the sequence.

Examples

			The sequence of all locally disjoint rooted identity trees preceded by their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   5: (((o)))
   6: (o(o))
  10: (o((o)))
  11: ((((o))))
  13: ((o(o)))
  15: ((o)((o)))
  22: (o(((o))))
  26: (o(o(o)))
  29: ((o((o))))
  30: (o(o)((o)))
  31: (((((o)))))
		

Crossrefs

Cf. A000081, A004111, A007097, A276625, A277098, A302696, A303362, A304713, A316467, A316471, A316474, A316495.

Programs

Mathematica

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