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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 July 15 02:31 EDT 2020. Contains 335762 sequences. (Running on oeis4.)