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

Author

Gus Wiseman, Nov 09 2019

Keywords

• nonn

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.

Examples

			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)
		

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.

Programs

Mathematica

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