A329139 - OEIS

%I #4 Nov 10 2019 20:29:26

%S 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,

%T 40,41,43,44,45,47,48,49,50,52,53,54,56,59,60,61,63,64,67,68,71,72,73,

%U 75,76,79,80,81,83,84,88,89,90,92,96,97,98,99,101,103,104

%N Numbers whose prime signature is an aperiodic word.

%C 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.

%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    1: ()

%e    2: (1)

%e    3: (1)

%e    4: (2)

%e    5: (1)

%e    7: (1)

%e    8: (3)

%e    9: (2)

%e   11: (1)

%e   12: (2,1)

%e   13: (1)

%e   16: (4)

%e   17: (1)

%e   18: (1,2)

%e   19: (1)

%e   20: (2,1)

%e   23: (1)

%e   24: (3,1)

%e   25: (2)

%e   27: (3)

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

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

%Y Complement of A329140.

%Y Aperiodic compositions are A000740.

%Y Aperiodic binary words are A027375.

%Y Numbers whose binary expansion is aperiodic are A328594.

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

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

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

%K nonn

%O 1,2

%A _Gus Wiseman_, Nov 09 2019