A291441 Matula-Goebel numbers of orderless same-trees with all leaves equal to 1.

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.

Links

Table of n, a(n) for n=1..41.

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