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A298120 Matula-Goebel numbers of rooted trees in which all positive outdegrees are odd. 9
1, 2, 3, 5, 8, 11, 12, 18, 19, 20, 27, 30, 31, 32, 37, 44, 45, 48, 50, 61, 66, 67, 71, 72, 75, 76, 80, 99, 103, 108, 110, 113, 114, 120, 124, 125, 127, 128, 131, 148, 157, 162, 165, 171, 176, 180, 186, 190, 192, 193, 197, 200, 222, 223, 229, 242, 243, 244, 264 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
EXAMPLE
Sequence of trees begins:
1 o
2 (o)
3 ((o))
5 (((o)))
8 (ooo)
11 ((((o))))
12 (oo(o))
18 (o(o)(o))
19 ((ooo))
20 (oo((o)))
27 ((o)(o)(o))
30 (o(o)((o)))
31 (((((o)))))
32 (ooooo)
37 ((oo(o)))
44 (oo(((o))))
45 ((o)(o)((o)))
48 (oooo(o))
50 (o((o))((o)))
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
otQ[n_]:=Or[n===1, With[{m=primeMS[n]}, OddQ@Length@m&&And@@otQ/@m]];
Select[Range[1000], otQ]
CROSSREFS
Sequence in context: A173672 A303024 A070223 * A298205 A117725 A106637
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 12 2018
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)