cp's OEIS Frontend

A317711 Numbers that are not uniform tree numbers.

%I A317711 #8 May 04 2021 20:51:57
%S A317711 12,18,20,24,28,37,40,44,45,48,50,52,54,56,60,61,63,68,71,72,74,75,76,
%T A317711 80,84,88,89,90,92,96,98,99,104,107,108,111,112,116,117,120,122,124,
%U A317711 126,132,135,136,140,142,144,147,148,150,152,153,156,157,160,162
%N A317711 Numbers that are not uniform tree numbers.
%C A317711 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.
%e A317711 The sequence of non-uniform tree numbers together with their Matula-Goebel trees begins:
%e A317711   12: (oo(o))
%e A317711   18: (o(o)(o))
%e A317711   20: (oo((o)))
%e A317711   24: (ooo(o))
%e A317711   28: (oo(oo))
%e A317711   37: ((oo(o)))
%e A317711   40: (ooo((o)))
%e A317711   44: (oo(((o))))
%e A317711   45: ((o)(o)((o)))
%e A317711   48: (oooo(o))
%e A317711   50: (o((o))((o)))
%e A317711   52: (oo(o(o)))
%e A317711   54: (o(o)(o)(o))
%e A317711   56: (ooo(oo))
%e A317711   60: (oo(o)((o)))
%t A317711 rupQ[n_]:=Or[n==1,And[SameQ@@FactorInteger[n][[All,2]],And@@rupQ/@PrimePi/@FactorInteger[n][[All,1]]]];
%t A317711 Select[Range[100],!rupQ[#]&]
%Y A317711 Cf. A061775, A072774, A111299, A214577, A276625, A277098, A303431, A317590.
%Y A317711 Cf. A317705, A317707, A317708, A317709, A317710 (complement), A317712, A317717, A317718.
%K A317711 nonn
%O A317711 1,1
%A A317711 _Gus Wiseman_, Aug 05 2018