cp's OEIS Frontend

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

%I A358508 #6 Nov 21 2022 09:48:02
%S A358508 1,6,12,24,48,30,192,104,148,72,3072,60,12288,832,144,712,196608,222,
%T A358508 786432,120,288,13312
%N A358508 Least Matula-Goebel number of a tree with exactly n permutations.
%C A358508 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.
%C A358508 To get a permutation of a tree, we choose a permutation of the multiset of branches of each node.
%e A358508 The terms together with their corresponding trees begin:
%e A358508       1: o
%e A358508       6: (o(o))
%e A358508      12: (oo(o))
%e A358508      24: (ooo(o))
%e A358508      48: (oooo(o))
%e A358508      30: (o(o)((o)))
%e A358508     192: (oooooo(o))
%e A358508     104: (ooo(o(o)))
%e A358508     148: (oo(oo(o)))
%e A358508      72: (ooo(o)(o))
%e A358508    3072: (oooooooooo(o))
%e A358508      60: (oo(o)((o)))
%e A358508   12288: (oooooooooooo(o))
%e A358508     832: (oooooo(o(o)))
%e A358508     144: (oooo(o)(o))
%e A358508     712: (ooo(ooo(o)))
%t A358508 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]
%t A358508 MGTree[n_Integer]:=If[n===1,{},MGTree/@primeMS[n]]
%t A358508 treeperms[t_]:=Times @@ Cases[t,b:{__}:>Length[Permutations[b]],{0,Infinity}];
%t A358508 uv=Table[treeperms[MGTree[n]],{n,100000}];
%t A358508 Table[Position[uv,k][[1,1]],{k,Min@@Complement[Range[Max@@uv],uv]-1}]
%Y A358508 Position of first appearance of n in A206487.
%Y A358508 The sorted version is A358507.
%Y A358508 A000081 counts rooted trees, ordered A000108.
%Y A358508 A214577 and A358377 rank trees with no permutations.
%Y A358508 Cf. A001263, A032027, A061775, A127301, A196050, A358378, A358506, A358521, A358522.
%K A358508 nonn,more
%O A358508 1,2
%A A358508 _Gus Wiseman_, Nov 20 2022