cp's OEIS Frontend

A317719 Numbers that are not powerful tree numbers.

%I A317719 #9 Sep 10 2018 23:44:48
%S A317719 6,10,12,13,14,15,18,20,21,22,24,26,28,29,30,33,34,35,37,38,39,40,41,
%T A317719 42,43,44,45,46,47,48,50,51,52,54,55,56,57,58,60,61,62,63,65,66,68,69,
%U A317719 70,71,73,74,75,76,77,78,79,80,82,84,85,86,87,88,89,90,91
%N A317719 Numbers that are not powerful tree numbers.
%C A317719 A positive integer n is a powerful tree number iff either n = 1 or n is a prime number whose prime index is a powerful tree number, or n is a powerful number (meaning its prime multiplicities are all greater than 1) whose prime indices are all powerful tree numbers. A prime index of n is a number m such that prime(m) divides n.
%e A317719 The sequence of numbers that are not powerful tree numbers together with their Matula-Goebel trees begins:
%e A317719    6: (o(o))
%e A317719   10: (o((o)))
%e A317719   12: (oo(o))
%e A317719   13: ((o(o)))
%e A317719   14: (o(oo))
%e A317719   15: ((o)((o)))
%e A317719   18: (o(o)(o))
%e A317719   20: (oo((o)))
%e A317719   21: ((o)(oo))
%e A317719   22: (o(((o))))
%e A317719   24: (ooo(o))
%e A317719   26: (o(o(o)))
%e A317719   28: (oo(oo))
%e A317719   29: ((o((o))))
%e A317719   30: (o(o)((o)))
%t A317719 powgoQ[n_]:=Or[n==1,If[PrimeQ[n],powgoQ[PrimePi[n]],And[Min@@FactorInteger[n][[All,2]]>1,And@@powgoQ/@PrimePi/@FactorInteger[n][[All,1]]]]];
%t A317719 Select[Range[100],!powgoQ[#]&]
%Y A317719 Complement of A318612.
%Y A317719 Cf. A000081, A001694, A061775, A111299, A214577, A276625, A277098, A303431.
%Y A317719 Cf. A317102, A317707, A317708, A317709, A317710, A317711, A317712, A317717, A317718.
%K A317719 nonn
%O A317719 1,1
%A A317719 _Gus Wiseman_, Aug 05 2018