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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A289078 for the definition of orderless same-tree. LINKS 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] CROSSREFS Cf. A007097, A109129, A214577, A280994, A289078, A289079, A291442, A291443. Sequence in context: A175341 A317705 A318692 * A331967 A301147 A131649 Adjacent sequences:  A291438 A291439 A291440 * A291442 A291443 A291444 KEYWORD nonn AUTHOR Gus Wiseman, Aug 23 2017 EXTENSIONS More terms from Jinyuan Wang, Jun 21 2020 STATUS approved

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Last modified August 6 15:15 EDT 2020. Contains 336248 sequences. (Running on oeis4.)