cp's OEIS Frontend

A316495 Matula-Goebel numbers of locally disjoint unlabeled rooted trees, meaning no branch overlaps any other (unequal) branch of the same root.

%I A316495 #6 Jul 05 2018 02:30:59
%S A316495 1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,22,24,26,28,29,30,
%T A316495 31,32,33,34,35,36,37,38,40,41,43,44,45,47,48,50,51,52,53,54,55,56,58,
%U A316495 59,60,61,62,64,66,67,68,70,71,72,74,75,76,77,79,80,82,85
%N A316495 Matula-Goebel numbers of locally disjoint unlabeled rooted trees, meaning no branch overlaps any other (unequal) branch of the same root.
%C A316495 A prime index of n is a number m such that prime(m) divides n. A number is in the sequence iff either it is equal to 1, it is a prime number whose prime index already belongs to the sequence, or its distinct prime indices are pairwise coprime and already belong to the sequence.
%e A316495 The sequence of all locally disjoint rooted trees preceded by their Matula-Goebel numbers begins:
%e A316495    1: o
%e A316495    2: (o)
%e A316495    3: ((o))
%e A316495    4: (oo)
%e A316495    5: (((o)))
%e A316495    6: (o(o))
%e A316495    7: ((oo))
%e A316495    8: (ooo)
%e A316495   10: (o((o)))
%e A316495   11: ((((o))))
%e A316495   12: (oo(o))
%e A316495   13: ((o(o)))
%e A316495   14: (o(oo))
%e A316495   15: ((o)((o)))
%e A316495   16: (oooo)
%e A316495   17: (((oo)))
%e A316495   18: (o(o)(o))
%e A316495   19: ((ooo))
%e A316495   20: (oo((o)))
%t A316495 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316495 go[n_]:=Or[n==1,And[Or[PrimeQ[n],CoprimeQ@@Union[primeMS[n]]],And@@go/@primeMS[n]]];
%t A316495 Select[Range[100],go]
%Y A316495 Cf. A000081, A007097, A302696, A303362, A304713, A316468, A316470, A316473, A316475, A316494.
%K A316495 nonn
%O A316495 1,2
%A A316495 _Gus Wiseman_, Jul 04 2018