A325663 Matula-Goebel numbers of not necessarily regular rooted stars.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 25, 27, 30, 31, 32, 33, 36, 40, 44, 45, 48, 50, 54, 55, 60, 62, 64, 66, 72, 75, 80, 81, 88, 90, 93, 96, 99, 100, 108, 110, 120, 121, 124, 125, 127, 128, 132, 135, 144, 150, 155, 160, 162, 165, 176

Offset

1,2

Comments

Products of members of A007097.

A rooted star is a rooted tree whose branches are all rooted paths.

Links

Table of n, a(n) for n=1..62.

Example

The sequence of rooted stars together with their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   4: (oo)
   5: (((o)))
   6: (o(o))
   8: (ooo)
   9: ((o)(o))
  10: (o((o)))
  11: ((((o))))
  12: (oo(o))
  15: ((o)((o)))
  16: (oooo)
  18: (o(o)(o))
  20: (oo((o)))
  22: (o(((o))))
  24: (ooo(o))
  25: (((o))((o)))
  27: ((o)(o)(o))
  30: (o(o)((o)))

Mathematica

rpQ[n_]:=n==1||PrimeQ[n]&&rpQ[PrimePi[n]];
Select[Range[100], And@@rpQ/@First/@FactorInteger[#]&]

Crossrefs

Cf. A007097, A056239, A061775, A109082, A109129, A112798, A196050, A324924, A325614, A325661, A325662.

Sequence in context: A067942 A130176 A156541 * A277620 A031143 A358521

Adjacent sequences: A325660 A325661 A325662 * A325664 A325665 A325666

Keyword

nonn

Author

Gus Wiseman, May 13 2019

Status

approved