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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
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
Sequence in context: A180333 A030364 A044967 * A011859 A032825 A251966
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 13 2018
STATUS
approved

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Last modified March 29 08:53 EDT 2024. Contains 371268 sequences. (Running on oeis4.)