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

1,2

Links

Table of n, a(n) for n=1..61.

Example

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)))))

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[#]&]

Crossrefs

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

Sequence in context: A327473 A326837 A326847 * A326534 A046686 A137944

Adjacent sequences: A298535 A298536 A298537 * A298539 A298540 A298541

Keyword

nonn

Author

Gus Wiseman, Jan 21 2018

Status

approved