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 A290760 Matula-Goebel numbers of transitive rooted identity trees (or transitive finitary sets). 26
 1, 2, 6, 30, 78, 330, 390, 870, 1410, 3198, 3390, 4290, 7878, 9570, 10230, 11310, 13026, 15510, 15990, 18330, 26070, 30966, 37290, 39390, 40890, 44070, 45210, 65130, 84810, 94830, 98310, 104610, 122070, 124410, 132990, 154830, 159330, 175890, 198330, 201630 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE Let o = {}. The sequence of transitive finitary sets begins: 1     o 2     {o} 6     {o,{o}} 30    {o,{o},{{o}}} 78    {o,{o},{o,{o}}} 330   {o,{o},{{o}},{{{o}}}} 390   {o,{o},{{o}},{o,{o}}} 870   {o,{o},{{o}},{o,{{o}}}} 1410  {o,{o},{{o}},{{o},{{o}}}} 3198  {o,{o},{o,{o}},{{o,{o}}}} 3390  {o,{o},{{o}},{o,{o},{{o}}}} 4290  {o,{o},{{o}},{{{o}}},{o,{o}}} 7878  {o,{o},{o,{o}},{o,{o,{o}}}} 9570  {o,{o},{{o}},{{{o}}},{o,{{o}}}} 10230 {o,{o},{{o}},{{{o}}},{{{{o}}}}} 11310 {o,{o},{{o}},{o,{o}},{o,{{o}}}} 13026 {o,{o},{o,{o}},{{o},{o,{o}}}} 15510 {o,{o},{{o}},{{{o}}},{{o},{{o}}}} 15990 {o,{o},{{o}},{o,{o}},{{o,{o}}}} 18330 {o,{o},{{o}},{o,{o}},{{o},{{o}}}} MATHEMATICA primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; finitaryQ[n_]:=finitaryQ[n]=Or[n===1, With[{m=primeMS[n]}, {UnsameQ@@m, finitaryQ/@m}]/.List->And]; subprimes[n_]:=If[n===1, {}, Union@@Cases[FactorInteger[n], {p_, _}:>FactorInteger[PrimePi[p]][[All, 1]]]]; transitaryQ[n_]:=Divisible[n, Times@@subprimes[n]]; nn=100000; Fold[Select, Range[nn], {finitaryQ, transitaryQ}] CROSSREFS Cf. A000081, A001192, A004111, A007097, A076146, A276625, A279861, A290689, A290822. Sequence in context: A174276 A117849 A328417 * A088857 A099081 A051844 Adjacent sequences:  A290757 A290758 A290759 * A290761 A290762 A290763 KEYWORD nonn AUTHOR Gus Wiseman, Oct 19 2017 STATUS approved

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Last modified May 28 10:49 EDT 2020. Contains 334681 sequences. (Running on oeis4.)