A325662 Matula-Goebel numbers of regular rooted stars.

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

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: A358459 A358377 A242175 * A275771 A118956 A109850

Adjacent sequences: A325659 A325660 A325661 * A325663 A325664 A325665

Keyword

nonn

Author

Gus Wiseman, May 13 2019

Status

approved