cp's OEIS Frontend

A318692 Matula-Goebel numbers of series-reduced powerful uniform rooted trees.

%I A318692 #7 Sep 02 2018 08:21:25
%S A318692 1,4,8,16,32,49,64,128,196,256,343,361,512,1024,1444,2048,2401,2744,
%T A318692 2809,4096,6859,8192,11236,16384,16807,17161,17689,32768,38416,51529,
%U A318692 54872,65536,68644,70756,96721,117649,130321,131072,137641,148877,206116,262144
%N A318692 Matula-Goebel numbers of series-reduced powerful uniform rooted trees.
%C A318692 A prime index of n is a number m such that prime(m) divides n. A positive integer n is a Matula-Goebel number of a series-reduced powerful uniform rooted tree iff either n = 1 or n is a squarefree number, whose prime indices are all Matula-Goebel numbers of series-reduced powerful uniform rooted trees, taken to a power > 1.
%e A318692 The sequence of all series-reduced powerful uniform rooted trees together with their Matula-Goebel numbers begins:
%e A318692     1: o
%e A318692     4: (oo)
%e A318692     8: (ooo)
%e A318692    16: (oooo)
%e A318692    32: (ooooo)
%e A318692    49: ((oo)(oo))
%e A318692    64: (oooooo)
%e A318692   128: (ooooooo)
%e A318692   196: (oo(oo)(oo))
%e A318692   256: (oooooooo)
%e A318692   343: ((oo)(oo)(oo))
%e A318692   361: ((ooo)(ooo))
%e A318692   512: (ooooooooo)
%t A318692 srpowunQ[n_]:=Or[n==1,And[SameQ@@FactorInteger[n][[All,2]],Min@@FactorInteger[n][[All,2]]>1,And@@srpowunQ/@PrimePi/@FactorInteger[n][[All,1]]]];
%t A318692 Select[Range[100000],srpowunQ]
%Y A318692 Cf. A000081, A001694, A061775, A072774, A214577, A291636, A317705, A317707, A317710, A318611, A318612, A318690, A318691.
%K A318692 nonn
%O A318692 1,2
%A A318692 _Gus Wiseman_, Aug 31 2018