OFFSET
1,1
COMMENTS
A positive integer n is a powerful tree number iff either n = 1 or n is a prime number whose prime index is a powerful tree number, or n is a powerful number (meaning its prime multiplicities are all greater than 1) whose prime indices are all powerful tree numbers. A prime index of n is a number m such that prime(m) divides n.
EXAMPLE
The sequence of numbers that are not powerful tree numbers together with their Matula-Goebel trees begins:
6: (o(o))
10: (o((o)))
12: (oo(o))
13: ((o(o)))
14: (o(oo))
15: ((o)((o)))
18: (o(o)(o))
20: (oo((o)))
21: ((o)(oo))
22: (o(((o))))
24: (ooo(o))
26: (o(o(o)))
28: (oo(oo))
29: ((o((o))))
30: (o(o)((o)))
MATHEMATICA
powgoQ[n_]:=Or[n==1, If[PrimeQ[n], powgoQ[PrimePi[n]], And[Min@@FactorInteger[n][[All, 2]]>1, And@@powgoQ/@PrimePi/@FactorInteger[n][[All, 1]]]]];
Select[Range[100], !powgoQ[#]&]
CROSSREFS
Complement of A318612.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved