OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. A number is in the sequence iff its distinct prime indices are pairwise indivisible and already belong to the sequence.
EXAMPLE
Sequence of locally stable rooted trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
7: ((oo))
8: (ooo)
9: ((o)(o))
11: ((((o))))
15: ((o)((o)))
16: (oooo)
17: (((oo)))
19: ((ooo))
23: (((o)(o)))
25: (((o))((o)))
27: ((o)(o)(o))
31: (((((o)))))
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Or[#==1, And[Select[Tuples[primeMS[#], 2], UnsameQ@@#&&Divisible@@#&]=={}, And@@#0/@primeMS[#]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 04 2018
STATUS
approved