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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved