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 A325662 Matula-Goebel numbers of regular rooted stars. 3
 1, 2, 3, 4, 5, 8, 9, 11, 16, 25, 27, 31, 32, 64, 81, 121, 125, 127, 128, 243, 256, 512, 625, 709, 729, 961, 1024, 1331, 2048, 2187, 3125, 4096, 5381, 6561, 8192, 14641, 15625, 16129, 16384, 19683, 29791, 32768, 52711, 59049, 65536, 78125, 131072, 161051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Powers of members of A007097. A regular rooted star is a rooted tree whose branches are all rooted paths of equal length. The number of terms <= 10^k, k=0,1,2,...: 1, 7, 15, 26, 35, 46, 56, 67, 76, 87, 98, 109, 121, 131, 142, 154, 163, 175, 185, 198, 208, 220, 231, 241, 254, 265, 275, etc. - Robert G. Wilson v, May 13 2019 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..275 (terms 1..48 from Gus Wiseman) EXAMPLE The sequence of regular rooted stars together with their Matula-Goebel numbers begins:     1: o     2: (o)     3: ((o))     4: (oo)     5: (((o)))     8: (ooo)     9: ((o)(o))    11: ((((o))))    16: (oooo)    25: (((o))((o)))    27: ((o)(o)(o))    31: (((((o)))))    32: (ooooo)    64: (oooooo)    81: ((o)(o)(o)(o))   121: ((((o)))(((o))))   125: (((o))((o))((o)))   127: ((((((o))))))   128: (ooooooo) MATHEMATICA rpQ[n_]:=n==1||PrimeQ[n]&&rpQ[PrimePi[n]]; Select[Range[100], #==1||PrimePowerQ[#]&&rpQ[FactorInteger[#][[1, 1]]]&] CROSSREFS Cf. A007097, A056239, A061775, A109082, A109129, A112798, A196050, A324924, A325614, A325661, A325663. Sequence in context: A083132 A302602 A242175 * A275771 A118956 A109850 Adjacent sequences:  A325659 A325660 A325661 * A325663 A325664 A325665 KEYWORD nonn AUTHOR Gus Wiseman, May 13 2019 STATUS approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)