A316468 Matula-Goebel numbers of locally stable rooted trees, meaning no branch is a submultiset of any other branch of the same root.

1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 16, 17, 19, 23, 25, 27, 31, 32, 33, 35, 45, 47, 49, 51, 53, 55, 59, 64, 67, 69, 75, 77, 81, 83, 85, 93, 95, 97, 99, 103, 119, 121, 125, 127, 128, 131, 135, 137, 141, 149, 153, 155, 161, 165, 175, 177, 187, 197, 201, 207, 209

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 its distinct prime indices are pairwise indivisible and already belong to the sequence.

Links

Table of n, a(n) for n=1..61.

Example

Sequence of locally stable rooted trees preceded by their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   7: ((oo))
   8: (ooo)
   9: ((o)(o))
  11: ((((o))))
  15: ((o)((o)))
  16: (oooo)
  17: (((oo)))
  19: ((ooo))
  23: (((o)(o)))
  25: (((o))((o)))
  27: ((o)(o)(o))
  31: (((((o)))))

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Or[#==1, And[Select[Tuples[primeMS[#], 2], UnsameQ@@#&&Divisible@@#&]=={}, And@@#0/@primeMS[#]]]&]

Crossrefs

Cf. A000081, A004111, A007097, A112798, A277098, A285572, A285573, A303362, A304713, A316467, A316470, A316473, A316475, A316476, A316495.

Sequence in context: A153730 A140691 A328668 * A099627 A324841 A184155

Adjacent sequences: A316465 A316466 A316467 * A316469 A316470 A316471

Keyword

nonn

Author

Gus Wiseman, Jul 04 2018

Status

approved