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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 17 2019
STATUS
approved