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A303024
Matula-Goebel numbers of anti-binary (no binary branchings) rooted trees.
6
1, 2, 3, 5, 8, 11, 12, 16, 18, 19, 20, 24, 27, 30, 31, 32, 36, 37, 40, 44, 45, 48, 50, 53, 54, 60, 61, 64, 66, 67, 71, 72, 75, 76, 80, 81, 88, 89, 90, 96, 99, 100, 103, 108, 110, 113, 114, 120, 124, 125, 127, 128, 131, 132, 135, 144, 148, 150, 151, 152, 157
OFFSET
1,2
EXAMPLE
The sequence of anti-binary rooted trees together with their Matula-Goebel numbers begins:
1: o
2: (o)
3: ((o))
5: (((o)))
8: (ooo)
11: ((((o))))
12: (oo(o))
16: (oooo)
18: (o(o)(o))
19: ((ooo))
20: (oo((o)))
24: (ooo(o))
27: ((o)(o)(o))
30: (o(o)((o)))
31: (((((o)))))
MATHEMATICA
abQ[n_]:=Or[n==1, And[PrimeOmega[n]!=2, And@@Cases[FactorInteger[n], {p_, _}:>abQ[PrimePi[p]]]]]
Select[Range[100], abQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 15 2018
STATUS
approved