OFFSET
1,1
COMMENTS
An unlabeled rooted tree is an identity tree if there are no repeated branches directly under the same root.
LINKS
EXAMPLE
The sequence of trees together with the Matula-Goebel numbers begins:
4: (oo)
7: ((oo))
8: (ooo)
12: (oo(o))
14: (o(oo))
16: (oooo)
17: (((oo)))
19: ((ooo))
20: (oo((o)))
21: ((o)(oo))
24: (ooo(o))
28: (oo(oo))
32: (ooooo)
34: (o((oo)))
35: (((o))(oo))
37: ((oo(o)))
38: (o(ooo))
40: (ooo((o)))
42: (o(o)(oo))
43: ((o(oo)))
MATHEMATICA
mgtree[n_]:=If[n==1, {}, mgtree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], And[!And@@Cases[mgtree[#], q:{__}:>UnsameQ@@q, {0, Infinity}], UnsameQ@@Cases[mgtree[#], {__}, {0, Infinity}]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 21 2019
STATUS
approved