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A317710
Uniform tree numbers. Matula-Goebel numbers of uniform rooted trees.
18
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
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]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 05 2018
STATUS
approved