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A317719
Numbers that are not powerful tree numbers.
4
6, 10, 12, 13, 14, 15, 18, 20, 21, 22, 24, 26, 28, 29, 30, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 82, 84, 85, 86, 87, 88, 89, 90, 91
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[#]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved