A329140 - OEIS

%I #4 Nov 10 2019 20:29:19

%S 6,10,14,15,21,22,26,30,33,34,35,36,38,39,42,46,51,55,57,58,62,65,66,

%T 69,70,74,77,78,82,85,86,87,91,93,94,95,100,102,105,106,110,111,114,

%U 115,118,119,122,123,129,130,133,134,138,141,142,143,145,146,154

%N Numbers whose prime signature is a periodic word.

%C First differs from A182853 in having 2100 = 2^2 * 3^1 * 5^2 * 7^1.

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

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

%e The sequence of terms together with their prime signatures begins:

%e    6: (1,1)

%e   10: (1,1)

%e   14: (1,1)

%e   15: (1,1)

%e   21: (1,1)

%e   22: (1,1)

%e   26: (1,1)

%e   30: (1,1,1)

%e   33: (1,1)

%e   34: (1,1)

%e   35: (1,1)

%e   36: (2,2)

%e   38: (1,1)

%e   39: (1,1)

%e   42: (1,1,1)

%e   46: (1,1)

%e   51: (1,1)

%e   55: (1,1)

%e   57: (1,1)

%e   58: (1,1)

%t aperQ[q_]:=Array[RotateRight[q,#1]&,Length[q],1,UnsameQ];

%t Select[Range[100],!aperQ[Last/@FactorInteger[#]]&]

%Y Complement of A329139.

%Y Periodic compositions are A178472.

%Y Periodic binary words are A152061.

%Y Numbers whose binary expansion is periodic are A121016.

%Y Numbers whose prime signature is a Lyndon word are A329131.

%Y Numbers whose prime signature is a necklace are A329138.

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Nov 09 2019