cp's OEIS Frontend

A329131 Numbers whose prime signature is a Lyndon word.

%I A329131 #8 Nov 10 2019 20:29:43
%S A329131 2,3,4,5,7,8,9,11,13,16,17,18,19,23,25,27,29,31,32,37,41,43,47,49,50,
%T A329131 53,54,59,61,64,67,71,73,75,79,81,83,89,97,98,101,103,107,108,109,113,
%U A329131 121,125,127,128,131,137,139,147,149,150,151,157,162,163,167
%N A329131 Numbers whose prime signature is a Lyndon word.
%C A329131 First differs from A133811 in having 50.
%C A329131 A Lyndon word is a finite sequence that is lexicographically strictly less than all of its cyclic rotations.
%C A329131 A number's prime signature is the sequence of positive exponents in its prime factorization.
%F A329131 Intersection of A329138 and A329139.
%e A329131 The prime signature of 30870 is (1,2,1,3), which is a Lyndon word, so 30870 is in the sequence.
%e A329131 The sequence of terms together with their prime indices begins:
%e A329131     2: {1}
%e A329131     3: {2}
%e A329131     4: {1,1}
%e A329131     5: {3}
%e A329131     7: {4}
%e A329131     8: {1,1,1}
%e A329131     9: {2,2}
%e A329131    11: {5}
%e A329131    13: {6}
%e A329131    16: {1,1,1,1}
%e A329131    17: {7}
%e A329131    18: {1,2,2}
%e A329131    19: {8}
%e A329131    23: {9}
%e A329131    25: {3,3}
%e A329131    27: {2,2,2}
%e A329131    29: {10}
%e A329131    31: {11}
%e A329131    32: {1,1,1,1,1}
%t A329131 lynQ[q_]:=Array[Union[{q,RotateRight[q,#]}]=={q,RotateRight[q,#]}&,Length[q]-1,1,And];
%t A329131 Select[Range[2,100],lynQ[Last/@FactorInteger[#]]&]
%Y A329131 Numbers whose reversed binary expansion is Lyndon are A328596.
%Y A329131 Numbers whose prime signature is a necklace are A329138.
%Y A329131 Numbers whose prime signature is aperiodic are A329139.
%Y A329131 Lyndon compositions are A059966.
%Y A329131 Prime signature is A124010.
%Y A329131 Cf. A000031, A000740, A000961, A001037, A025487, A027375, A097318, A112798, A118914, A304678, A318731, A329140, A329142.
%K A329131 nonn
%O A329131 1,1
%A A329131 _Gus Wiseman_, Nov 06 2019