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A316494
Matula-Goebel numbers of locally disjoint rooted identity trees, meaning no branch overlaps any other branch of the same root.
9
1, 2, 3, 5, 6, 10, 11, 13, 15, 22, 26, 29, 30, 31, 33, 41, 47, 55, 58, 62, 66, 79, 82, 93, 94, 101, 109, 110, 113, 123, 127, 137, 141, 143, 145, 155, 158, 165, 179, 186, 202, 205, 211, 218, 226, 246, 254, 257, 271, 274, 282, 286, 290, 293, 310, 317, 327, 330
OFFSET
1,2
COMMENTS
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 prime indices are pairwise coprime, distinct, and already belong to the sequence.
EXAMPLE
The sequence of all locally disjoint rooted identity trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
5: (((o)))
6: (o(o))
10: (o((o)))
11: ((((o))))
13: ((o(o)))
15: ((o)((o)))
22: (o(((o))))
26: (o(o(o)))
29: ((o((o))))
30: (o(o)((o)))
31: (((((o)))))
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Or[#==1, And[SquareFreeQ[#], Or[PrimeQ[#], CoprimeQ@@primeMS[#]], And@@#0/@primeMS[#]]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 04 2018
STATUS
approved