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A117975
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Triangle where a(1,1)=1; a(n,m) = number of positive integers which are missing from row (n-1) of the triangle, are <= n and are coprime to m.
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1
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1, 1, 0, 2, 1, 1, 2, 1, 1, 1, 3, 2, 2, 2, 2, 4, 2, 3, 2, 3, 2, 4, 3, 3, 3, 3, 3, 3, 6, 3, 5, 3, 5, 3, 5, 3, 6, 3, 5, 3, 6, 2, 5, 3, 5, 6, 3, 5, 3, 5, 2, 5, 3, 5, 3, 7, 4, 6, 4, 6, 3, 6, 4, 6, 4, 6, 8, 4, 6, 4, 6, 3, 8, 4, 6, 3, 7, 3, 8, 5, 6, 5, 6, 4, 8, 5, 6, 4, 7, 4, 7, 9, 5, 6, 5, 8, 3, 8, 5, 6, 5, 8, 3, 8, 5, 10, 5, 8, 5, 8, 4
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OFFSET
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1,4
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LINKS
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EXAMPLE
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Row 5 of the triangle is [3,2,2,2,2]. There are 4 positive integers (1,4,5,6) which are coprime to 1, are <= 6 and are not among the terms of row 5. There are 2 positive integers (1,5) which are <= 6, are coprime to 2 and are not among the terms of row 5. ...(Skipping over the m = 3, 4 and 5 cases.) There are 2 positive integer (1,5) which are <= 6, are coprime to 6 and do not occur in row 5.
So row 6 is [4,2,3,2,3,2].
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MATHEMATICA
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prev = {1}; Flatten[Join[{prev}, Table[prev = Table[Length[Select[Complement[Range[n], prev], CoprimeQ[#, m] &]], {m, n}], {n, 2, 14}]]] (* T. D. Noe, Mar 30 2011 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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