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A291441
Matula-Goebel numbers of orderless same-trees with all leaves equal to 1.
12
1, 4, 8, 16, 32, 49, 64, 128, 256, 343, 361, 512, 1024, 2048, 2401, 2809, 4096, 6859, 8192, 12031, 16384, 16807, 17161, 32768, 51529, 65536, 96721, 117649, 130321, 131072, 148877, 262144, 516961, 524288, 637643, 718099, 757907, 823543, 1048576, 2097152, 2248091
OFFSET
1,2
COMMENTS
See A289078 for the definition of orderless same-tree.
EXAMPLE
a(20)=12031 corresponds to the following same-tree: {{1,1,1,1},{{1,1},{1,1}}}.
MATHEMATICA
nn=200000;
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
leafcount[n_]:=If[n===1, 1, With[{m=primeMS[n]}, If[Length[m]===1, leafcount[First[m]], Total[leafcount/@m]]]];
sameQ[n_]:=Or[n===1, With[{m=primeMS[n]}, And[Length[m]>1, SameQ@@leafcount/@m, And@@sameQ/@m]]];
Select[Range[nn], sameQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 23 2017
EXTENSIONS
More terms from Jinyuan Wang, Jun 21 2020
STATUS
approved