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A318731
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Number of relatively prime Lyndon compositions (aperiodic necklaces of positive integers) with sum n.
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11
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1, 0, 1, 2, 5, 7, 17, 27, 54, 93, 185, 324, 629, 1143, 2175, 4050, 7709, 14469, 27593, 52276, 99839, 190371, 364721, 698508, 1342170, 2580165, 4970952, 9585232, 18512789, 35787985, 69273665, 134211600, 260300799, 505278705, 981706783
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OFFSET
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1,4
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LINKS
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FORMULA
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EXAMPLE
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The a(6) = 7 relatively prime Lyndon compositions are 15, 114, 132, 123, 1113, 1122, 11112.
The a(7) = 17 relatively prime Lyndon compositions:
16, 25, 34,
115, 142, 124, 133, 223,
1114, 1213, 1132, 1123, 1222,
11113, 11212, 11122,
111112.
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MATHEMATICA
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LyndonQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]&&Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], LyndonQ[#]&&GCD@@#==1&]], {n, 10}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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