A316502 Matula-Goebel numbers of unlabeled rooted trees with n nodes in which the branches of any node with more than one branch have empty intersection.

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, 42, 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, 78, 79, 80

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 either it is a prime or its prime indices are relatively prime, and its prime indices already belong to the sequence.

Links

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

Index entries for sequences related to Matula-Göbel numbers

Example

Sequence of 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)

Mathematica

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

Crossrefs

Cf. A000081, A000837, A007097, A276625, A289509, A302796, A316468, A316470, A316495, A316501, A316502.

Sequence in context: A327534 A305732 A265999 * A316495 A356316 A036741

Adjacent sequences: A316499 A316500 A316501 * A316503 A316504 A316505

Keyword

nonn

Author

Gus Wiseman, Jul 05 2018

Status

approved