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A317709
Aperiodic relatively prime tree numbers. Matula-Goebel numbers of aperiodic relatively prime trees.
10
1, 2, 3, 5, 6, 10, 11, 12, 13, 15, 18, 20, 22, 24, 26, 29, 30, 31, 33, 37, 40, 41, 44, 45, 47, 48, 50, 52, 54, 55, 58, 60, 61, 62, 66, 71, 72, 74, 75, 78, 79, 80, 82, 88, 89, 90, 93, 94, 96, 99, 101, 104, 108, 109, 110, 113, 116, 120, 122, 123, 124, 127, 130
OFFSET
1,2
COMMENTS
A positive integer n is in the sequence iff either n = 1 or n is a prime number whose prime index already belongs to the sequence or n is not a perfect power and its prime indices are relatively prime numbers already belonging to the sequence. A prime index of n is a number m such that prime(m) divides n.
EXAMPLE
The sequence of aperiodic relatively prime tree numbers together with their Matula-Goebel trees begins:
1: o
2: (o)
3: ((o))
5: (((o)))
6: (o(o))
10: (o((o)))
11: ((((o))))
12: (oo(o))
13: ((o(o)))
15: ((o)((o)))
18: (o(o)(o))
20: (oo((o)))
22: (o(((o))))
24: (ooo(o))
26: (o(o(o)))
29: ((o((o))))
30: (o(o)((o)))
31: (((((o)))))
MATHEMATICA
rupQ[n_]:=Or[n==1, If[PrimeQ[n], rupQ[PrimePi[n]], And[GCD@@FactorInteger[n][[All, 2]]==1, GCD@@PrimePi/@FactorInteger[n][[All, 1]]==1, And@@rupQ/@PrimePi/@FactorInteger[n][[All, 1]]]]];
Select[Range[100], rupQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved