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A334298 Numbers whose prime signature is a reversed Lyndon word.

%I A334298 #4 Jun 10 2020 14:06:17
%S A334298 1,2,3,4,5,7,8,9,11,12,13,16,17,19,20,23,24,25,27,28,29,31,32,37,40,
%T A334298 41,43,44,45,47,48,49,52,53,56,59,60,61,63,64,67,68,71,72,73,76,79,80,
%U A334298 81,83,84,88,89,92,96,97,99,101,103,104,107,109,112,113,116
%N A334298 Numbers whose prime signature is a reversed Lyndon word.
%C A334298 A Lyndon word is a finite sequence that is lexicographically strictly less than all of its cyclic rotations.
%C A334298 A number's prime signature is the sequence of positive exponents in its prime factorization.
%e A334298 The prime signature of 4200 is (3,1,2,1), which is a reversed Lyndon word, so 4200 is in the sequence.
%e A334298 The sequence of terms together with their prime indices begins:
%e A334298    1: {}           23: {9}            48: {1,1,1,1,2}
%e A334298    2: {1}          24: {1,1,1,2}      49: {4,4}
%e A334298    3: {2}          25: {3,3}          52: {1,1,6}
%e A334298    4: {1,1}        27: {2,2,2}        53: {16}
%e A334298    5: {3}          28: {1,1,4}        56: {1,1,1,4}
%e A334298    7: {4}          29: {10}           59: {17}
%e A334298    8: {1,1,1}      31: {11}           60: {1,1,2,3}
%e A334298    9: {2,2}        32: {1,1,1,1,1}    61: {18}
%e A334298   11: {5}          37: {12}           63: {2,2,4}
%e A334298   12: {1,1,2}      40: {1,1,1,3}      64: {1,1,1,1,1,1}
%e A334298   13: {6}          41: {13}           67: {19}
%e A334298   16: {1,1,1,1}    43: {14}           68: {1,1,7}
%e A334298   17: {7}          44: {1,1,5}        71: {20}
%e A334298   19: {8}          45: {2,2,3}        72: {1,1,1,2,2}
%e A334298   20: {1,1,3}      47: {15}           73: {21}
%t A334298 lynQ[q_]:=Length[q]==0||Array[Union[{q,RotateRight[q,#1]}]=={q,RotateRight[q,#1]}&,Length[q]-1,1,And];
%t A334298 Select[Range[100],lynQ[Reverse[Last/@If[#==1,{},FactorInteger[#]]]]&]
%Y A334298 The non-reversed version is A329131.
%Y A334298 Lyndon compositions are A059966.
%Y A334298 Prime signature is A124010.
%Y A334298 Numbers with strictly decreasing prime multiplicities are A304686.
%Y A334298 Numbers whose reversed binary expansion is Lyndon are A328596.
%Y A334298 Numbers whose prime signature is a necklace are A329138.
%Y A334298 Numbers whose prime signature is aperiodic are A329139.
%Y A334298 Cf. A000031, A000740, A000961, A001037, A025487, A027375, A097318, A112798, A118914, A304678, A318731, A329140, A329142.
%K A334298 nonn
%O A334298 1,2
%A A334298 _Gus Wiseman_, Jun 10 2020