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A317711
Numbers that are not uniform tree numbers.
9
12, 18, 20, 24, 28, 37, 40, 44, 45, 48, 50, 52, 54, 56, 60, 61, 63, 68, 71, 72, 74, 75, 76, 80, 84, 88, 89, 90, 92, 96, 98, 99, 104, 107, 108, 111, 112, 116, 117, 120, 122, 124, 126, 132, 135, 136, 140, 142, 144, 147, 148, 150, 152, 153, 156, 157, 160, 162
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[#]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved