|
|
A316468
|
|
Matula-Goebel numbers of locally stable rooted trees, meaning no branch is a submultiset of any other branch of the same root.
|
|
10
|
|
|
1, 2, 3, 4, 5, 7, 8, 9, 11, 15, 16, 17, 19, 23, 25, 27, 31, 32, 33, 35, 45, 47, 49, 51, 53, 55, 59, 64, 67, 69, 75, 77, 81, 83, 85, 93, 95, 97, 99, 103, 119, 121, 125, 127, 128, 131, 135, 137, 141, 149, 153, 155, 161, 165, 175, 177, 187, 197, 201, 207, 209
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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 its distinct prime indices are pairwise indivisible and already belong to the sequence.
|
|
LINKS
|
|
|
EXAMPLE
|
Sequence of locally stable rooted trees preceded by their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
7: ((oo))
8: (ooo)
9: ((o)(o))
11: ((((o))))
15: ((o)((o)))
16: (oooo)
17: (((oo)))
19: ((ooo))
23: (((o)(o)))
25: (((o))((o)))
27: ((o)(o)(o))
31: (((((o)))))
|
|
MATHEMATICA
|
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Or[#==1, And[Select[Tuples[primeMS[#], 2], UnsameQ@@#&&Divisible@@#&]=={}, And@@#0/@primeMS[#]]]&]
|
|
CROSSREFS
|
Cf. A000081, A004111, A007097, A112798, A277098, A285572, A285573, A303362, A304713, A316467, A316470, A316473, A316475, A316476, A316495.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|