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

Author

Gus Wiseman, Aug 23 2017

Keywords

• nonn

Comments

See A289078 for the definition of orderless same-tree.

Examples

			a(20)=12031 corresponds to the following same-tree: {{1,1,1,1},{{1,1},{1,1}}}.
		

Crossrefs

Cf. A007097, A109129, A214577, A280994, A289078, A289079, A291442, A291443.

Programs

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]

Extensions

More terms from Jinyuan Wang, Jun 21 2020