OFFSET
1,2
COMMENTS
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.
EXAMPLE
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.
Sequence of locally stable rooted identity trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
5: (((o)))
11: ((((o))))
15: ((o)((o)))
31: (((((o)))))
33: ((o)(((o))))
47: (((o)((o))))
55: (((o))(((o))))
93: ((o)((((o)))))
127: ((((((o))))))
137: (((o)(((o)))))
141: ((o)((o)((o))))
155: (((o))((((o)))))
165: ((o)((o))(((o))))
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
ain[n_]:=And[Select[Tuples[primeMS[n], 2], UnsameQ@@#&&Divisible@@#&]=={}, SquareFreeQ[n], And@@ain/@primeMS[n]];
Select[Range[100], ain]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 04 2018
STATUS
approved