A316521 Matula-Goebel numbers of rooted trees where all terminal rooted subtrees are either constant or strict.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 62, 64, 65, 66, 67, 69, 70, 73, 77, 78, 79, 81, 82, 83, 85, 86, 87, 91, 93, 94, 95, 97, 101

Offset

1,2

Comments

The following are equivalent.

1. n is in the sequence.

2. prime(n) is in the sequence.

3. n is a product of prime numbers that are already in the sequence and that are either all equal or all different.

Links

Table of n, a(n) for n=1..67.

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
go[n_]:=And[Or[SameQ@@primeMS[n], UnsameQ@@primeMS[n]], And@@go/@primeMS[n]]
Select[Range[100], go]

Crossrefs

Cf. A000081, A000961, A003238, A004111, A005117, A007097, A072774, A214577, A276625, A277098.

Sequence in context: A317710 A303554 A325328 * A085156 A342522 A102466

Adjacent sequences: A316518 A316519 A316520 * A316522 A316523 A316524

Keyword

nonn

Author

Gus Wiseman, Jul 05 2018

Status

approved