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 A318690 Matula-Goebel numbers of powerful uniform rooted trees. 3
 1, 2, 3, 4, 5, 7, 8, 9, 11, 16, 17, 19, 23, 25, 27, 31, 32, 36, 49, 53, 59, 64, 67, 81, 83, 97, 100, 103, 121, 125, 127, 128, 131, 151, 196, 216, 225, 227, 241, 243, 256, 277, 289, 311, 331, 343, 361, 419, 431, 441, 484, 509, 512, 529, 541, 563, 625, 661, 691 (list; graph; refs; listen; history; text; internal format)
 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 powerful uniform rooted tree iff either n = 1 or n is a prime number whose prime index is a Matula-Goebel number of a powerful uniform rooted tree or n is a squarefree number taken to a power > 1 whose prime indices are all Matula-Goebel numbers of powerful uniform rooted trees. LINKS Gus Wiseman, The first 96 powerful uniform rooted trees. EXAMPLE The sequence of all powerful uniform rooted trees together with their Matula-Goebel numbers begins:    1: o    2: (o)    3: ((o))    4: (oo)    5: (((o)))    7: ((oo))    8: (ooo)    9: ((o)(o))   11: ((((o))))   16: (oooo)   17: (((oo)))   19: ((ooo))   23: (((o)(o)))   25: (((o))((o)))   27: ((o)(o)(o))   31: (((((o)))))   32: (ooooo)   36: (oo(o)(o))   49: ((oo)(oo)) MATHEMATICA powunQ[n_]:=Or[n==1, If[PrimeQ[n], powunQ[PrimePi[n]], And[SameQ@@FactorInteger[n][[All, 2]], Min@@FactorInteger[n][[All, 2]]>1, And@@powunQ/@PrimePi/@FactorInteger[n][[All, 1]]]]]; Select[Range[100], powunQ] CROSSREFS Cf. A000081, A001694, A061775, A072774, A214577, A317705, A317707, A317710, A317717, A317719, A318611, A318612, A318689, A318692. Sequence in context: A184155 A331913 A318612 * A302498 A243497 A214577 Adjacent sequences:  A318687 A318688 A318689 * A318691 A318692 A318693 KEYWORD nonn AUTHOR Gus Wiseman, Aug 31 2018 STATUS approved

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Last modified April 7 01:11 EDT 2020. Contains 333291 sequences. (Running on oeis4.)