A358508 Least Matula-Goebel number of a tree with exactly n permutations.

1, 6, 12, 24, 48, 30, 192, 104, 148, 72, 3072, 60, 12288, 832, 144, 712, 196608, 222, 786432, 120, 288, 13312

Offset

1,2

Comments

The Matula-Goebel number of a rooted tree is the product of primes indexed by the Matula-Goebel numbers of the branches of its root, which gives a bijective correspondence between positive integers and unlabeled rooted trees.

To get a permutation of a tree, we choose a permutation of the multiset of branches of each node.

Links

Table of n, a(n) for n=1..22.

Example

The terms together with their corresponding trees begin:
      1: o
      6: (o(o))
     12: (oo(o))
     24: (ooo(o))
     48: (oooo(o))
     30: (o(o)((o)))
    192: (oooooo(o))
    104: (ooo(o(o)))
    148: (oo(oo(o)))
     72: (ooo(o)(o))
   3072: (oooooooooo(o))
     60: (oo(o)((o)))
  12288: (oooooooooooo(o))
    832: (oooooo(o(o)))
    144: (oooo(o)(o))
    712: (ooo(ooo(o)))

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]
MGTree[n_Integer]:=If[n===1, {}, MGTree/@primeMS[n]]
treeperms[t_]:=Times @@ Cases[t, b:{__}:>Length[Permutations[b]], {0, Infinity}];
uv=Table[treeperms[MGTree[n]], {n, 100000}];
Table[Position[uv, k][[1, 1]], {k, Min@@Complement[Range[Max@@uv], uv]-1}]

Crossrefs

Position of first appearance of n in A206487.

The sorted version is A358507.

A000081 counts rooted trees, ordered A000108.

A214577 and A358377 rank trees with no permutations.

Cf. A001263, A032027, A061775, A127301, A196050, A358378, A358506, A358521, A358522.

Sequence in context: A090765 A199910 A210678 * A304938 A297107 A330997

Adjacent sequences: A358505 A358506 A358507 * A358509 A358510 A358511

Keyword

nonn,more

Author

Gus Wiseman, Nov 20 2022

Status

approved