cp's OEIS Frontend

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.

%I A319270 #7 Sep 17 2018 08:34:05
%S A319270 1,2,6,12,18,24,26,48,52,54,72,74,78,96,104,108,122,148,156,162,178,
%T A319270 192,202,208,222,234,244,288,296,312,338,356,366,384,404,416,432,444,
%U A319270 446,468,478,486,488,502,534,592,606,624,648,666,702,712,718,732,746
%N 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.
%C A319270 Also Matula-Goebel numbers of series-reduced locally non-intersecting aperiodic rooted trees.
%e A319270 The sequence of Matula-Goebel trees of elements of this sequence begins:
%e A319270    1: o
%e A319270    2: (o)
%e A319270    6: (o(o))
%e A319270   12: (oo(o))
%e A319270   18: (o(o)(o))
%e A319270   24: (ooo(o))
%e A319270   26: (o(o(o)))
%e A319270   48: (oooo(o))
%e A319270   52: (oo(o(o)))
%e A319270   54: (o(o)(o)(o))
%e A319270   72: (ooo(o)(o))
%e A319270   74: (o(oo(o)))
%e A319270   78: (o(o)(o(o)))
%e A319270   96: (ooooo(o))
%t A319270 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A319270 ain[n_]:=Or[n==1,And[GCD@@primeMS[n]==1,GCD@@Length/@Split[primeMS[n]]==1,And@@ain/@primeMS[n]]];
%t A319270 Select[Range[100],ain]
%Y A319270 Cf. A000081, A007097, A061775, A276625, A298748, A301700, A303431, A316470, A319271.
%K A319270 nonn
%O A319270 1,2
%A A319270 _Gus Wiseman_, Sep 16 2018