A329140 Numbers whose prime signature is a periodic word.

6, 10, 14, 15, 21, 22, 26, 30, 33, 34, 35, 36, 38, 39, 42, 46, 51, 55, 57, 58, 62, 65, 66, 69, 70, 74, 77, 78, 82, 85, 86, 87, 91, 93, 94, 95, 100, 102, 105, 106, 110, 111, 114, 115, 118, 119, 122, 123, 129, 130, 133, 134, 138, 141, 142, 143, 145, 146, 154

Offset

1,1

Comments

First differs from A182853 in having 2100 = 2^2 * 3^1 * 5^2 * 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..59.

Example

The sequence of terms together with their prime signatures begins:
   6: (1,1)
  10: (1,1)
  14: (1,1)
  15: (1,1)
  21: (1,1)
  22: (1,1)
  26: (1,1)
  30: (1,1,1)
  33: (1,1)
  34: (1,1)
  35: (1,1)
  36: (2,2)
  38: (1,1)
  39: (1,1)
  42: (1,1,1)
  46: (1,1)
  51: (1,1)
  55: (1,1)
  57: (1,1)
  58: (1,1)

Mathematica

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

Crossrefs

Complement of A329139.

Periodic compositions are A178472.

Periodic binary words are A152061.

Numbers whose binary expansion is periodic are A121016.

Numbers whose prime signature is a Lyndon word are A329131.

Numbers whose prime signature is a necklace are A329138.

Cf. A025487, A056239, A097318, A112798, A118914, A124010, A181819, A304678, A329132 A329134, A329143, A329144.

Sequence in context: A362606 A130092 A289619 * A362605 A182853 A212168

Adjacent sequences: A329137 A329138 A329139 * A329141 A329142 A329143

Keyword

nonn

Author

Gus Wiseman, Nov 09 2019

Status

approved