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A298126 Matula-Goebel numbers of rooted trees in which all outdegrees are even. 4
1, 4, 14, 16, 49, 56, 64, 86, 106, 196, 224, 256, 301, 344, 371, 424, 454, 526, 622, 686, 784, 886, 896, 1024, 1154, 1204, 1376, 1484, 1589, 1696, 1816, 1841, 1849, 2104, 2177, 2279, 2386, 2401, 2488, 2744, 2809, 2846, 3101, 3136, 3238, 3544, 3584, 3986, 4039 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

Sequence of trees begins:

1   o

4   (oo)

14  (o(oo))

16  (oooo)

49  ((oo)(oo))

56  (ooo(oo))

64  (oooooo)

86  (o(o(oo)))

106 (o(oooo))

196 (oo(oo)(oo))

224 (ooooo(oo))

256 (oooooooo)

301 ((oo)(o(oo)))

344 (ooo(o(oo)))

371 ((oo)(oooo))

424 (ooo(oooo))

454 (o((oo)(oo)))

526 (o(ooo(oo)))

622 (o(oooooo))

686 (o(oo)(oo)(oo))

784 (oooo(oo)(oo))

886 (o(o(o(oo))))

896 (ooooooo(oo))

MATHEMATICA

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

etQ[n_]:=Or[n===1, With[{m=primeMS[n]}, EvenQ@Length@m&&And@@etQ/@m]];

Select[Range[10000], etQ]

CROSSREFS

Cf. A000081, A001190, A007097, A026424, A028260, A061775, A111299, A214577, A245824, A276625, A277098, A290760, A291441, A291442, A291636, A295461, A297571, A298118, A298120.

Sequence in context: A180333 A030364 A044967 * A011859 A032825 A251966

Adjacent sequences:  A298123 A298124 A298125 * A298127 A298128 A298129

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 13 2018

STATUS

approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)