%I #8 Aug 05 2018 20:42:28
%S 1,2,3,4,5,6,7,8,10,11,13,14,15,16,17,19,22,26,29,30,31,32,33,34,35,
%T 36,38,41,42,43,47,51,53,55,58,59,62,64,66,67,70,77,78,79,82,85,86,93,
%U 94,95,100,101,102,105,106,109,110,113,114,118,119,123,127,128
%N Uniform relatively prime tree numbers. Matula-Goebel numbers of uniform relatively prime rooted trees.
%C 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.
%H A. David Christopher and M. Davamani Christober, <a href="http://emis.impa.br/EMIS/journals/GMN/yahoo_site_admin/assets/docs/1_GMN-2492-V13N2.77213831.pdf">Relatively Prime Uniform Partitions</a>, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp.1-12.
%t 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 Select[Range[200],rupQ]
%Y Cf. A000081, A061775, A072774, A214577, A276625, A277098, A317588.
%Y Cf. A317705, A317707, A317708, A317709, A317710, A317711, A317712, A317718.
%K nonn
%O 1,2
%A _Gus Wiseman_, Aug 05 2018