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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

Table of n, a(n) for n=1..59.

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

Cf. A000081, A007097, A026424, A061775, A214577, A276625, A277098, A290760, A291441, A291442, A291636, A297571, A298118.

Sequence in context: A173672 A303024 A070223 * A298205 A117725 A106637

Adjacent sequences:  A298117 A298118 A298119 * A298121 A298122 A298123

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 12 2018

STATUS

approved

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Last modified April 6 16:14 EDT 2020. Contains 333276 sequences. (Running on oeis4.)