(Translated by https://www.hiragana.jp/)
# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a316467 Showing 1-1 of 1 %I A316467 #7 Jul 04 2018 20:24:57 %S A316467 1,2,3,5,11,15,31,33,47,55,93,127,137,141,155,165,211,257,341,381,411, %T A316467 465,487,633,635,709,771,773,811,907,977,1023,1055,1285,1297,1397, %U A316467 1457,1461,1507,1621,1705,1905,2127,2293,2319,2321,2433,2621,2721,2833,2931 %N A316467 Matula-Goebel numbers of locally stable rooted identity trees, meaning no branch is a subset of any other branch of the same root. %C A316467 A prime index of n is a number m such that prime(m) divides n. A number belongs to this sequence iff it is squarefree, its distinct prime indices are pairwise indivisible, and its prime indices also belong to this sequence. %e A316467 165 = prime(2)*prime(3)*prime(5) belongs to the sequence because it is squarefree, the indices {2,3,5} are pairwise indivisible, and each of them already belongs to the sequence. %e A316467 Sequence of locally stable rooted identity trees preceded by their Matula-Goebel numbers begins: %e A316467 1: o %e A316467 2: (o) %e A316467 3: ((o)) %e A316467 5: (((o))) %e A316467 11: ((((o)))) %e A316467 15: ((o)((o))) %e A316467 31: (((((o))))) %e A316467 33: ((o)(((o)))) %e A316467 47: (((o)((o)))) %e A316467 55: (((o))(((o)))) %e A316467 93: ((o)((((o))))) %e A316467 127: ((((((o)))))) %e A316467 137: (((o)(((o))))) %e A316467 141: ((o)((o)((o)))) %e A316467 155: (((o))((((o))))) %e A316467 165: ((o)((o))(((o)))) %t A316467 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]; %t A316467 ain[n_]:=And[Select[Tuples[primeMS[n],2],UnsameQ@@#&&Divisible@@#&]=={},SquareFreeQ[n],And@@ain/@primeMS[n]]; %t A316467 Select[Range[100],ain] %Y A316467 Cf. A000081, A004111, A007097, A276625, A277098, A285572, A285573, A302796, A303362, A304713, A316468, A316469, A316471, A316474, A316476, A316494. %K A316467 nonn %O A316467 1,2 %A A316467 _Gus Wiseman_, Jul 04 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE