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A324766
Matula-Goebel numbers of recursively anti-transitive rooted trees.
9
1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 16, 17, 19, 20, 21, 22, 23, 25, 27, 29, 31, 32, 33, 34, 35, 40, 44, 46, 49, 50, 51, 53, 57, 59, 62, 63, 64, 67, 68, 71, 73, 77, 79, 80, 81, 83, 85, 87, 88, 92, 93, 95, 97, 99, 100, 103, 109, 115, 118, 121, 124, 125, 127, 128
OFFSET
1,2
COMMENTS
The complement is {6, 12, 13, 14, 15, 18, 24, 26, 28, 30, 36, ...}.
An unlabeled rooted tree is recursively anti-transitive if no branch of a branch of a terminal subtree is a branch of the same subtree.
EXAMPLE
The sequence of recursively anti-transitive rooted trees together with their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
4: (oo)
5: (((o)))
7: ((oo))
8: (ooo)
9: ((o)(o))
10: (o((o)))
11: ((((o))))
16: (oooo)
17: (((oo)))
19: ((ooo))
20: (oo((o)))
21: ((o)(oo))
22: (o(((o))))
23: (((o)(o)))
25: (((o))((o)))
27: ((o)(o)(o))
29: ((o((o))))
31: (((((o)))))
32: (ooooo)
33: ((o)(((o))))
34: (o((oo)))
35: (((o))(oo))
40: (ooo((o)))
44: (oo(((o))))
46: (o((o)(o)))
49: ((oo)(oo))
50: (o((o))((o)))
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
totantiQ[n_]:=And[Intersection[Union@@primeMS/@primeMS[n], primeMS[n]]=={}, And@@totantiQ/@primeMS[n]];
Select[Range[100], totantiQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved