OFFSET
1,1
COMMENTS
An unlabeled rooted tree is locally nonintersecting if there is no common subbranch to all branches directly under any given node.
EXAMPLE
The sequence of rooted trees that are not locally nonintersecting together with their Matula-Goebel numbers begins:
9: ((o)(o))
21: ((o)(oo))
23: (((o)(o)))
25: (((o))((o)))
27: ((o)(o)(o))
39: ((o)(o(o)))
46: (o((o)(o)))
49: ((oo)(oo))
57: ((o)(ooo))
63: ((o)(o)(oo))
65: (((o))(o(o)))
69: ((o)((o)(o)))
73: (((o)(oo)))
81: ((o)(o)(o)(o))
83: ((((o)(o))))
87: ((o)(o((o))))
91: ((oo)(o(o)))
92: (oo((o)(o)))
97: ((((o))((o))))
MATHEMATICA
rupQ[n_]:=Or[n==1, If[PrimeQ[n], rupQ[PrimePi[n]], And[GCD@@PrimePi/@FactorInteger[n][[All, 1]]==1, And@@rupQ/@PrimePi/@FactorInteger[n][[All, 1]]]]];
Select[Range[100], !rupQ[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 07 2018
STATUS
approved