cp's OEIS Frontend

A358554 Least Matula-Goebel number of a rooted tree with n internal (non-leaf) nodes.

%I A358554 #5 Nov 27 2022 08:56:00
%S A358554 1,2,3,5,11,25,55,121,275,605,1331,3025,6655,14641,33275,73205
%N A358554 Least Matula-Goebel number of a rooted tree with n internal (non-leaf) nodes.
%C A358554 Positions of first appearances in A342507.
%C A358554 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.
%e A358554 The terms together with their corresponding rooted trees begin:
%e A358554       1: o
%e A358554       2: (o)
%e A358554       3: ((o))
%e A358554       5: (((o)))
%e A358554      11: ((((o))))
%e A358554      25: (((o))((o)))
%e A358554      55: (((o))(((o))))
%e A358554     121: ((((o)))(((o))))
%e A358554     275: (((o))((o))(((o))))
%e A358554     605: (((o))(((o)))(((o))))
%e A358554    1331: ((((o)))(((o)))(((o))))
%e A358554    3025: (((o))((o))(((o)))(((o))))
%e A358554    6655: (((o))(((o)))(((o)))(((o))))
%e A358554   14641: ((((o)))(((o)))(((o)))(((o))))
%e A358554   33275: (((o))((o))(((o)))(((o)))(((o))))
%e A358554   73205: (((o))(((o)))(((o)))(((o)))(((o))))
%t A358554 MGTree[n_]:=If[n==1,{},MGTree/@Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A358554 seq=Table[Count[MGTree[n],_[__],{0,Infinity}],{n,1000}];
%t A358554 Table[Position[seq,n][[1,1]],{n,Union[seq]}]
%Y A358554 For height instead of internals we have A007097, firsts of A109082.
%Y A358554 For leaves instead of internals we have A151821, firsts of A109129.
%Y A358554 Positions of first appearances in A342507.
%Y A358554 The ordered version gives firsts of A358553.
%Y A358554 A000081 counts rooted trees, ordered A000108.
%Y A358554 A034781 counts rooted trees by nodes and height.
%Y A358554 A055277 counts rooted trees by nodes and leaves.
%Y A358554 MG statistics: A061775, A109082, A109129, A196050, A342507, A358552.
%Y A358554 Cf. A000040, A000720, A001222, A007097, A056239, A112798.
%Y A358554 Cf. A001263, A206487, A358578, A358592.
%K A358554 nonn,more
%O A358554 1,2
%A A358554 _Gus Wiseman_, Nov 27 2022