cp's OEIS Frontend

A290760 Matula-Goebel numbers of transitive rooted identity trees (or transitive finitary sets).

%I A290760 #14 Oct 20 2017 15:40:40
%S A290760 1,2,6,30,78,330,390,870,1410,3198,3390,4290,7878,9570,10230,11310,
%T A290760 13026,15510,15990,18330,26070,30966,37290,39390,40890,44070,45210,
%U A290760 65130,84810,94830,98310,104610,122070,124410,132990,154830,159330,175890,198330,201630
%N A290760 Matula-Goebel numbers of transitive rooted identity trees (or transitive finitary sets).
%C A290760 A rooted tree is transitive if every terminal subtree is a branch of the root. A finitary set is transitive if every element is also a subset.
%e A290760 Let o = {}. The sequence of transitive finitary sets begins:
%e A290760 1     o
%e A290760 2     {o}
%e A290760 6     {o,{o}}
%e A290760 30    {o,{o},{{o}}}
%e A290760 78    {o,{o},{o,{o}}}
%e A290760 330   {o,{o},{{o}},{{{o}}}}
%e A290760 390   {o,{o},{{o}},{o,{o}}}
%e A290760 870   {o,{o},{{o}},{o,{{o}}}}
%e A290760 1410  {o,{o},{{o}},{{o},{{o}}}}
%e A290760 3198  {o,{o},{o,{o}},{{o,{o}}}}
%e A290760 3390  {o,{o},{{o}},{o,{o},{{o}}}}
%e A290760 4290  {o,{o},{{o}},{{{o}}},{o,{o}}}
%e A290760 7878  {o,{o},{o,{o}},{o,{o,{o}}}}
%e A290760 9570  {o,{o},{{o}},{{{o}}},{o,{{o}}}}
%e A290760 10230 {o,{o},{{o}},{{{o}}},{{{{o}}}}}
%e A290760 11310 {o,{o},{{o}},{o,{o}},{o,{{o}}}}
%e A290760 13026 {o,{o},{o,{o}},{{o},{o,{o}}}}
%e A290760 15510 {o,{o},{{o}},{{{o}}},{{o},{{o}}}}
%e A290760 15990 {o,{o},{{o}},{o,{o}},{{o,{o}}}}
%e A290760 18330 {o,{o},{{o}},{o,{o}},{{o},{{o}}}}
%t A290760 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A290760 finitaryQ[n_]:=finitaryQ[n]=Or[n===1,With[{m=primeMS[n]},{UnsameQ@@m,finitaryQ/@m}]/.List->And];
%t A290760 subprimes[n_]:=If[n===1,{},Union@@Cases[FactorInteger[n],{p_,_}:>FactorInteger[PrimePi[p]][[All,1]]]];
%t A290760 transitaryQ[n_]:=Divisible[n,Times@@subprimes[n]];
%t A290760 nn=100000;Fold[Select,Range[nn],{finitaryQ,transitaryQ}]
%Y A290760 Cf. A000081, A001192, A004111, A007097, A076146, A276625, A279861, A290689, A290822.
%K A290760 nonn
%O A290760 1,2
%A A290760 _Gus Wiseman_, Oct 19 2017