A298538 Matula-Goebel numbers of rooted trees such that every branch of the root has the same number of nodes.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 175, 179, 181, 187

Offset: 1

Author

Gus Wiseman, Jan 21 2018

Keywords

• nonn

Examples

			Sequence of trees begins:
1  o
2  (o)
3  ((o))
4  (oo)
5  (((o)))
7  ((oo))
8  (ooo)
9  ((o)(o))
11 ((((o))))
13 ((o(o)))
16 (oooo)
17 (((oo)))
19 ((ooo))
23 (((o)(o)))
25 (((o))((o)))
27 ((o)(o)(o))
29 ((o((o))))
31 (((((o)))))
		

Crossrefs

Cf. A000081, A007097, A061775, A111299, A214577, A276625, A290760, A291442, A297571, A298478, A298534, A298536, A298537.

Programs

Mathematica

nn=500;
primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
MGweight[n_]:=If[n===1,1,1+Total[MGweight/@primeMS[n]]];
Select[Range[nn],SameQ@@MGweight/@primeMS[#]&]