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%I #10 May 04 2021 20:52:20
%S 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,29,30,31,
%T 32,33,34,35,36,38,39,41,42,43,46,47,49,51,53,55,57,58,59,62,64,65,66,
%U 67,69,70,73,77,78,79,81,82,83,85,86,87,91,93,94,95,97
%N Uniform tree numbers. Matula-Goebel numbers of uniform rooted trees.
%C A positive integer n is a uniform tree number iff either n = 1 or n is a power of a squarefree number whose prime indices are also uniform 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,And[SameQ@@FactorInteger[n][[All,2]],And@@rupQ/@PrimePi/@FactorInteger[n][[All,1]]]];
%t Select[Range[100],rupQ]
%Y Cf. A061775, A072774, A111299, A214577, A276625, A277098, A303431, A317589.
%Y Cf. A317705, A317707, A317708, A317709, A317711 (complement), A317712, A317717, A317718.
%K nonn
%O 1,2
%A _Gus Wiseman_, Aug 05 2018
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