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%I #16 Sep 25 2018 11:55:18
%S 2,3,2,5,3,2,7,4,3,2,11,6,4,3,2,13,7,5,4,3,2,19,10,7,5,4,3,2,23,12,8,
%T 6,5,4,3,2,29,15,10,8,6,5,4,3,2,33,17,12,9,7,6,5,4,3,2,43,22,15,11,9,
%U 7,6,5,4,3,2,47,24,16,12,10,8,7,6,5,4,3,2
%N Triangular array T read by rows: T(n,k) is the number of Farey fractions of order n that are <= 1/k for k=1..n, for n>=1.
%C So, T(n, k) is also the index of fraction 1/k in the Farey fractions of order n. - _Michel Marcus_, Jun 27 2014
%e Rows: {2}; {3,2}; {5,3,2}; ...; e.g. in row 3, 5 reduced fractions (0/1,1/3,1/2,2/3,1/1) are <=1; 3 are <=1/2; 2 are <=1/3.
%e Triangle starts:
%e 2;
%e 3, 2;
%e 5, 3, 2;
%e 7, 4, 3, 2;
%e 11, 6, 4, 3, 2;
%e 13, 7, 5, 4, 3, 2;
%e ...
%t T[n_, k_] := Count[FareySequence[n], f_ /; f <= 1/k];
%t Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 25 2018 *)
%o (PARI) row(nn) = my(frow = farey(n)); for (k=1, n, print1(vecsearch(frow, 1/k), ", ");); \\ _Michel Marcus_, Jun 27 2014
%Y First column: T(n, 1) = A005728(n+1).
%Y Cf. A006842, A006843.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_
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