OFFSET
1,1
COMMENTS
A positive integer n is a uniform tree number iff either n = 1 or n is a power of a squarefree number whose prime indices are also uniform tree numbers. A prime index of n is a number m such that prime(m) divides n.
EXAMPLE
The sequence of non-uniform tree numbers together with their Matula-Goebel trees begins:
12: (oo(o))
18: (o(o)(o))
20: (oo((o)))
24: (ooo(o))
28: (oo(oo))
37: ((oo(o)))
40: (ooo((o)))
44: (oo(((o))))
45: ((o)(o)((o)))
48: (oooo(o))
50: (o((o))((o)))
52: (oo(o(o)))
54: (o(o)(o)(o))
56: (ooo(oo))
60: (oo(o)((o)))
MATHEMATICA
rupQ[n_]:=Or[n==1, And[SameQ@@FactorInteger[n][[All, 2]], And@@rupQ/@PrimePi/@FactorInteger[n][[All, 1]]]];
Select[Range[100], !rupQ[#]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved