A317711 - OEIS

%I #8 May 04 2021 20:51:57

%S 12,18,20,24,28,37,40,44,45,48,50,52,54,56,60,61,63,68,71,72,74,75,76,

%T 80,84,88,89,90,92,96,98,99,104,107,108,111,112,116,117,120,122,124,

%U 126,132,135,136,140,142,144,147,148,150,152,153,156,157,160,162

%N Numbers that are not uniform tree numbers.

%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.

%e The sequence of non-uniform tree numbers together with their Matula-Goebel trees begins:

%e   12: (oo(o))

%e   18: (o(o)(o))

%e   20: (oo((o)))

%e   24: (ooo(o))

%e   28: (oo(oo))

%e   37: ((oo(o)))

%e   40: (ooo((o)))

%e   44: (oo(((o))))

%e   45: ((o)(o)((o)))

%e   48: (oooo(o))

%e   50: (o((o))((o)))

%e   52: (oo(o(o)))

%e   54: (o(o)(o)(o))

%e   56: (ooo(oo))

%e   60: (oo(o)((o)))

%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, A317590.

%Y Cf. A317705, A317707, A317708, A317709, A317710 (complement), A317712, A317717, A317718.

%K nonn

%O 1,1

%A _Gus Wiseman_, Aug 05 2018