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%I #7 Sep 17 2018 08:34:05
%S 1,2,6,12,18,24,26,48,52,54,72,74,78,96,104,108,122,148,156,162,178,
%T 192,202,208,222,234,244,288,296,312,338,356,366,384,404,416,432,444,
%U 446,468,478,486,488,502,534,592,606,624,648,666,702,712,718,732,746
%N Numbers that are 1 or whose prime indices are relatively prime and belong to the sequence, and whose prime multiplicities are also relatively prime.
%C Also Matula-Goebel numbers of series-reduced locally non-intersecting aperiodic rooted trees.
%e The sequence of Matula-Goebel trees of elements of this sequence begins:
%e 1: o
%e 2: (o)
%e 6: (o(o))
%e 12: (oo(o))
%e 18: (o(o)(o))
%e 24: (ooo(o))
%e 26: (o(o(o)))
%e 48: (oooo(o))
%e 52: (oo(o(o)))
%e 54: (o(o)(o)(o))
%e 72: (ooo(o)(o))
%e 74: (o(oo(o)))
%e 78: (o(o)(o(o)))
%e 96: (ooooo(o))
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t ain[n_]:=Or[n==1,And[GCD@@primeMS[n]==1,GCD@@Length/@Split[primeMS[n]]==1,And@@ain/@primeMS[n]]];
%t Select[Range[100],ain]
%Y Cf. A000081, A007097, A061775, A276625, A298748, A301700, A303431, A316470, A319271.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 16 2018
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