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%I #17 Feb 03 2022 12:41:59
%S 0,1,3,6,12,21,35,58,106,188,243,493,593,1062,3275,5507,5803,12426,
%T 12915,42410,131772,167587,168841,428012,839367,1015501,1968161,
%U 5787286
%N Number of partitions of 1 into fractions i/j with 1<=i<j<=n and i,j coprime.
%F A115856(n) = a(n+1) - a(n).
%e 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.
%t 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 *)
%t 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 *)
%Y Cf. A002966, A000041, A000010.
%Y Cf. A116084, A038566, A038567, A115856.
%K nonn,more
%O 1,3
%A _Reinhard Zumkeller_, Feb 01 2006
%E More terms from _Michael De Vlieger_, Jul 15 2016
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