OFFSET
1,2
COMMENTS
Also Matula-Goebel numbers of series-reduced locally non-intersecting aperiodic rooted trees.
EXAMPLE
The sequence of Matula-Goebel trees of elements of this sequence begins:
1: o
2: (o)
6: (o(o))
12: (oo(o))
18: (o(o)(o))
24: (ooo(o))
26: (o(o(o)))
48: (oooo(o))
52: (oo(o(o)))
54: (o(o)(o)(o))
72: (ooo(o)(o))
74: (o(oo(o)))
78: (o(o)(o(o)))
96: (ooooo(o))
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
ain[n_]:=Or[n==1, And[GCD@@primeMS[n]==1, GCD@@Length/@Split[primeMS[n]]==1, And@@ain/@primeMS[n]]];
Select[Range[100], ain]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 16 2018
STATUS
approved