cp's OEIS Frontend

A317720 Numbers that are not uniform relatively prime tree numbers.

%I A317720 #4 Aug 05 2018 20:42:47
%S A317720 9,12,18,20,21,23,24,25,27,28,37,39,40,44,45,46,48,49,50,52,54,56,57,
%T A317720 60,61,63,65,68,69,71,72,73,74,75,76,80,81,83,84,87,88,89,90,91,92,96,
%U A317720 97,98,99,103,104,107,108,111,112,115,116,117,120,121,122,124
%N A317720 Numbers that are not uniform relatively prime tree numbers.
%C A317720 A positive integer n is a uniform relatively prime tree number iff either n = 1 or n is a prime number whose prime index is a uniform relatively prime tree number, or n is a power of a squarefree number whose prime indices are relatively prime and are themselves uniform relatively prime tree numbers. A prime index of n is a number m such that prime(m) divides n.
%e A317720 The sequence of non-uniform tree numbers together with their Matula-Goebel trees begins:
%e A317720    9: ((o)(o))
%e A317720   12: (oo(o))
%e A317720   18: (o(o)(o))
%e A317720   20: (oo((o)))
%e A317720   21: ((o)(oo))
%e A317720   23: (((o)(o)))
%e A317720   24: (ooo(o))
%e A317720   25: (((o))((o)))
%e A317720   27: ((o)(o)(o))
%e A317720   28: (oo(oo))
%e A317720   37: ((oo(o)))
%e A317720   39: ((o)(o(o)))
%e A317720   40: (ooo((o)))
%e A317720   44: (oo(((o))))
%e A317720   45: ((o)(o)((o)))
%t A317720 rupQ[n_]:=Or[n==1,If[PrimeQ[n],rupQ[PrimePi[n]],And[SameQ@@FactorInteger[n][[All,2]],GCD@@PrimePi/@FactorInteger[n][[All,1]]==1,And@@rupQ/@PrimePi/@FactorInteger[n][[All,1]]]]];
%t A317720 Select[Range[200],!rupQ[#]&]
%Y A317720 Cf. A061775, A072774, A111299, A214577, A276625, A277098, A303431, A317590.
%Y A317720 Cf. A317705, A317707, A317708, A317709, A317710, A317712, A317717, A317718.
%K A317720 nonn
%O A317720 1,1
%A A317720 _Gus Wiseman_, Aug 05 2018