A316495 Matula-Goebel numbers of locally disjoint unlabeled rooted trees, meaning no branch overlaps any other (unequal) branch of the same root.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 70, 71, 72, 74, 75, 76, 77, 79, 80, 82, 85

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

Links

Table of n, a(n) for n=1..67.

Example

The sequence of all locally disjoint rooted trees preceded by their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   6: (o(o))
   7: ((oo))
   8: (ooo)
  10: (o((o)))
  11: ((((o))))
  12: (oo(o))
  13: ((o(o)))
  14: (o(oo))
  15: ((o)((o)))
  16: (oooo)
  17: (((oo)))
  18: (o(o)(o))
  19: ((ooo))
  20: (oo((o)))

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
go[n_]:=Or[n==1, And[Or[PrimeQ[n], CoprimeQ@@Union[primeMS[n]]], And@@go/@primeMS[n]]];
Select[Range[100], go]

Crossrefs

Cf. A000081, A007097, A302696, A303362, A304713, A316468, A316470, A316473, A316475, A316494.

Sequence in context: A305732 A265999 A316502 * A356316 A036741 A037479

Adjacent sequences: A316492 A316493 A316494 * A316496 A316497 A316498

Keyword

nonn

Author

Gus Wiseman, Jul 04 2018

Status

approved