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A298424
Matula-Goebel numbers of rooted trees in which all positive outdegrees are the same.
7
1, 2, 3, 4, 5, 8, 11, 14, 16, 31, 32, 49, 64, 76, 86, 127, 128, 256, 301, 424, 454, 512, 709, 722, 886, 1024, 1532, 1589, 1849, 2048, 2096, 3101, 3986, 4096, 5381, 6418, 6859, 8192, 9761, 9952, 11236, 13766, 13951, 14554, 16384, 19049, 21884, 22463, 23512
OFFSET
1,2
EXAMPLE
Sequence of trees begins:
1 o
2 (o)
3 ((o))
4 (oo)
5 (((o)))
8 (ooo)
11 ((((o))))
14 (o(oo))
16 (oooo)
31 (((((o)))))
32 (ooooo)
49 ((oo)(oo))
64 (oooooo)
76 (oo(ooo))
86 (o(o(oo)))
127 ((((((o))))))
128 (ooooooo)
256 (oooooooo)
301 ((oo)(o(oo)))
424 (ooo(oooo))
454 (o((oo)(oo)))
512 (ooooooooo)
709 (((((((o)))))))
722 (o(ooo)(ooo))
886 (o(o(o(oo))))
MATHEMATICA
MGtree[n_]:=If[n===1, {}, MGtree/@Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
soQ[n_]:=Or[n===1, SameQ@@Length/@Cases[MGtree[n], {__}, {0, Infinity}]];
Select[Range[1000], soQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 19 2018
STATUS
approved