A049806 Number of Farey fractions of order n that are <=1/2; cf. A049805.

1, 2, 3, 4, 6, 7, 10, 12, 15, 17, 22, 24, 30, 33, 37, 41, 49, 52, 61, 65, 71, 76, 87, 91, 101, 107, 116, 122, 136, 140, 155, 163, 173, 181, 193, 199, 217, 226, 238, 246, 266, 272, 293, 303, 315, 326, 349, 357, 378, 388, 404, 416, 442

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Partial sums + 1 of A023022.

Cf. A005728, A049807, A049808, A049809, A049810, A049811, A049812, A049813, A049814.

Programs

Mathematica

Farey[n_] := Union[Flatten[Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; f[n_] := Length@ Select[ Farey@ n, # <= 1/2 &]; Array[f, 53] (* Robert G. Wilson v, Nov 14 2012 *)
a[n_] := Count[FareySequence[n], f_ /; f <= 1/2]; Array[a, 53] (* Jean-François Alcover, Sep 25 2018 *)