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A318692
Matula-Goebel numbers of series-reduced powerful uniform rooted trees.
3
1, 4, 8, 16, 32, 49, 64, 128, 196, 256, 343, 361, 512, 1024, 1444, 2048, 2401, 2744, 2809, 4096, 6859, 8192, 11236, 16384, 16807, 17161, 17689, 32768, 38416, 51529, 54872, 65536, 68644, 70756, 96721, 117649, 130321, 131072, 137641, 148877, 206116, 262144
OFFSET
1,2
COMMENTS
A prime index of n is a number m such that prime(m) divides n. A positive integer n is a Matula-Goebel number of a series-reduced powerful uniform rooted tree iff either n = 1 or n is a squarefree number, whose prime indices are all Matula-Goebel numbers of series-reduced powerful uniform rooted trees, taken to a power > 1.
EXAMPLE
The sequence of all series-reduced powerful uniform rooted trees together with their Matula-Goebel numbers begins:
1: o
4: (oo)
8: (ooo)
16: (oooo)
32: (ooooo)
49: ((oo)(oo))
64: (oooooo)
128: (ooooooo)
196: (oo(oo)(oo))
256: (oooooooo)
343: ((oo)(oo)(oo))
361: ((ooo)(ooo))
512: (ooooooooo)
MATHEMATICA
srpowunQ[n_]:=Or[n==1, And[SameQ@@FactorInteger[n][[All, 2]], Min@@FactorInteger[n][[All, 2]]>1, And@@srpowunQ/@PrimePi/@FactorInteger[n][[All, 1]]]];
Select[Range[100000], srpowunQ]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 31 2018
STATUS
approved