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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
OFFSET
1,2
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 13 2018
STATUS
approved