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A115855
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Number of partitions of 1 into fractions i/j with 1<=i<j<=n and i,j coprime.
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3
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0, 1, 3, 6, 12, 21, 35, 58, 106, 188, 243, 493, 593, 1062, 3275, 5507, 5803, 12426, 12915, 42410, 131772, 167587, 168841, 428012, 839367, 1015501, 1968161, 5787286
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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a(4) = #{1/2+1/2, 1/2+1/4+1/4, 1/3+2/3, 1/3+1/3+1/3, 1/4+3/4, 1/4+1/4+1/4+1/4} = 6.
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MATHEMATICA
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Table[Length@ Select[Flatten[Map[IntegerPartitions[1, {#}, Rest@ Union[Flatten@ TensorProduct[#, 1/#] &@ Range@ n /. {_Integer -> 0, k_ /; k > 1 -> 0}]] &, Range@ n], 1], Total@ # == 1 &], {n, 25}] (* Michael De Vlieger, Jul 15 2016 *) (* or *)
a[n_] := Sum[ Length@ IntegerPartitions[1, {k}, Union@ Flatten[ Table[i/j, {j, n}, {i, j-1}]]], {k, n}]; Array[a, 20] (* Giovanni Resta, Jun 15 2017 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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