cp's OEIS Frontend

A317709 Aperiodic relatively prime tree numbers. Matula-Goebel numbers of aperiodic relatively prime trees.

%I A317709 #6 Aug 05 2018 08:24:50
%S A317709 1,2,3,5,6,10,11,12,13,15,18,20,22,24,26,29,30,31,33,37,40,41,44,45,
%T A317709 47,48,50,52,54,55,58,60,61,62,66,71,72,74,75,78,79,80,82,88,89,90,93,
%U A317709 94,96,99,101,104,108,109,110,113,116,120,122,123,124,127,130
%N A317709 Aperiodic relatively prime tree numbers. Matula-Goebel numbers of aperiodic relatively prime trees.
%C A317709 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.
%e A317709 The sequence of aperiodic relatively prime tree numbers together with their Matula-Goebel trees begins:
%e A317709    1: o
%e A317709    2: (o)
%e A317709    3: ((o))
%e A317709    5: (((o)))
%e A317709    6: (o(o))
%e A317709   10: (o((o)))
%e A317709   11: ((((o))))
%e A317709   12: (oo(o))
%e A317709   13: ((o(o)))
%e A317709   15: ((o)((o)))
%e A317709   18: (o(o)(o))
%e A317709   20: (oo((o)))
%e A317709   22: (o(((o))))
%e A317709   24: (ooo(o))
%e A317709   26: (o(o(o)))
%e A317709   29: ((o((o))))
%e A317709   30: (o(o)((o)))
%e A317709   31: (((((o)))))
%t A317709 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]]]]];
%t A317709 Select[Range[100],rupQ]
%Y A317709 Cf. A000081, A061775, A111299, A214577, A276625, A277098, A301700, A303431, A316503.
%Y A317709 Cf. A317705, A317707, A317708, A317710, A317711, A317712.
%K A317709 nonn
%O A317709 1,2
%A A317709 _Gus Wiseman_, Aug 05 2018