A317710 Uniform tree numbers. Matula-Goebel numbers of uniform rooted trees.

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, 36, 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

Offset

1,2

Comments

A positive integer n is a uniform tree number iff either n = 1 or n is a power of a squarefree number whose prime indices are also uniform tree numbers. A prime index of n is a number m such that prime(m) divides n.

Links

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

A. David Christopher and M. Davamani Christober, Relatively Prime Uniform Partitions, Gen. Math. Notes, Vol. 13, No. 2, December, 2012, pp.1-12.

Mathematica

rupQ[n_]:=Or[n==1, And[SameQ@@FactorInteger[n][[All, 2]], And@@rupQ/@PrimePi/@FactorInteger[n][[All, 1]]]];
Select[Range[100], rupQ]

Crossrefs

Cf. A061775, A072774, A111299, A214577, A276625, A277098, A303431, A317589.

Cf. A317705, A317707, A317708, A317709, A317711 (complement), A317712, A317717, A317718.

Sequence in context: A062770 A359889 A236510 * A303554 A325328 A316521

Adjacent sequences: A317707 A317708 A317709 * A317711 A317712 A317713

Keyword

nonn

Author

Gus Wiseman, Aug 05 2018

Status

approved