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A319270
Numbers that are 1 or whose prime indices are relatively prime and belong to the sequence, and whose prime multiplicities are also relatively prime.
1
1, 2, 6, 12, 18, 24, 26, 48, 52, 54, 72, 74, 78, 96, 104, 108, 122, 148, 156, 162, 178, 192, 202, 208, 222, 234, 244, 288, 296, 312, 338, 356, 366, 384, 404, 416, 432, 444, 446, 468, 478, 486, 488, 502, 534, 592, 606, 624, 648, 666, 702, 712, 718, 732, 746
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 16 2018
STATUS
approved