A329139 Numbers whose prime signature is an aperiodic word.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 37, 40, 41, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 56, 59, 60, 61, 63, 64, 67, 68, 71, 72, 73, 75, 76, 79, 80, 81, 83, 84, 88, 89, 90, 92, 96, 97, 98, 99, 101, 103, 104

Offset

1,2

Comments

First differs from A319161 in having 1260 = 2*2 * 3^2 * 5^1 * 7^1. First differs from A325370 in having 420 = 2^2 * 3^1 * 5^1 * 7^1.

A number's prime signature (A124010) is the sequence of positive exponents in its prime factorization.

A sequence is aperiodic if its cyclic rotations are all different.

Links

Table of n, a(n) for n=1..66.

Example

The sequence of terms together with their prime signatures begins:
   1: ()
   2: (1)
   3: (1)
   4: (2)
   5: (1)
   7: (1)
   8: (3)
   9: (2)
  11: (1)
  12: (2,1)
  13: (1)
  16: (4)
  17: (1)
  18: (1,2)
  19: (1)
  20: (2,1)
  23: (1)
  24: (3,1)
  25: (2)
  27: (3)

Mathematica

aperQ[q_]:=Array[RotateRight[q, #1]&, Length[q], 1, UnsameQ];
Select[Range[100], aperQ[Last/@FactorInteger[#]]&]

Crossrefs

Complement of A329140.

Aperiodic compositions are A000740.

Aperiodic binary words are A027375.

Numbers whose binary expansion is aperiodic are A328594.

Numbers whose prime signature is a Lyndon word are A329131.

Numbers whose prime signature is a necklace are A329138.

Cf. A025487, A097318, A112798, A124010, A178472, A181819, A304678, A329133, A329135, A329136, A329137, A329142.

Sequence in context: A344586 A319161 A325370 * A356862 A351294 A130091

Adjacent sequences: A329136 A329137 A329138 * A329140 A329141 A329142

Keyword

nonn

Author

Gus Wiseman, Nov 09 2019

Status

approved