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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 31 2018
STATUS
approved