cp's OEIS Frontend

A329139 Numbers whose prime signature is an aperiodic word.

%I A329139 #4 Nov 10 2019 20:29:26
%S A329139 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 A329139 40,41,43,44,45,47,48,49,50,52,53,54,56,59,60,61,63,64,67,68,71,72,73,
%U A329139 75,76,79,80,81,83,84,88,89,90,92,96,97,98,99,101,103,104
%N A329139 Numbers whose prime signature is an aperiodic word.
%C A329139 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 A329139 A number's prime signature (A124010) is the sequence of positive exponents in its prime factorization.
%C A329139 A sequence is aperiodic if its cyclic rotations are all different.
%e A329139 The sequence of terms together with their prime signatures begins:
%e A329139    1: ()
%e A329139    2: (1)
%e A329139    3: (1)
%e A329139    4: (2)
%e A329139    5: (1)
%e A329139    7: (1)
%e A329139    8: (3)
%e A329139    9: (2)
%e A329139   11: (1)
%e A329139   12: (2,1)
%e A329139   13: (1)
%e A329139   16: (4)
%e A329139   17: (1)
%e A329139   18: (1,2)
%e A329139   19: (1)
%e A329139   20: (2,1)
%e A329139   23: (1)
%e A329139   24: (3,1)
%e A329139   25: (2)
%e A329139   27: (3)
%t A329139 aperQ[q_]:=Array[RotateRight[q,#1]&,Length[q],1,UnsameQ];
%t A329139 Select[Range[100],aperQ[Last/@FactorInteger[#]]&]
%Y A329139 Complement of A329140.
%Y A329139 Aperiodic compositions are A000740.
%Y A329139 Aperiodic binary words are A027375.
%Y A329139 Numbers whose binary expansion is aperiodic are A328594.
%Y A329139 Numbers whose prime signature is a Lyndon word are A329131.
%Y A329139 Numbers whose prime signature is a necklace are A329138.
%Y A329139 Cf. A025487, A097318, A112798, A124010, A178472, A181819, A304678, A329133, A329135, A329136, A329137, A329142.
%K A329139 nonn
%O A329139 1,2
%A A329139 _Gus Wiseman_, Nov 09 2019