A317717 Uniform relatively prime tree numbers. Matula-Goebel numbers of uniform relatively prime rooted trees.

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 22, 26, 29, 30, 31, 32, 33, 34, 35, 36, 38, 41, 42, 43, 47, 51, 53, 55, 58, 59, 62, 64, 66, 67, 70, 77, 78, 79, 82, 85, 86, 93, 94, 95, 100, 101, 102, 105, 106, 109, 110, 113, 114, 118, 119, 123, 127, 128

Offset: 1

Author

Gus Wiseman, Aug 05 2018

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A000081, A061775, A072774, A214577, A276625, A277098, A317588.

Cf. A317705, A317707, A317708, A317709, A317710, A317711, A317712, A317718.

Programs

Mathematica

rupQ[n_]:=Or[n==1,If[PrimeQ[n],rupQ[PrimePi[n]],And[SameQ@@FactorInteger[n][[All,2]],GCD@@PrimePi/@FactorInteger[n][[All,1]]==1,And@@rupQ/@PrimePi/@FactorInteger[n][[All,1]]]]];
Select[Range[200],rupQ]