  Franel and Landau derived an arithmetic statement involving the Farey
sequence that is equivalent to the Riemann hypothesis. Since there is a
relationship between the Mertens function and the Riemann hypothesis, there
should be a relationship between the Mertens function and the Farey sequence.
Functions of subsets of the fractions in Farey sequences that are analogous to
the Mertens function are introduced. Mikolas proved that the sum of certain
Mertens function values is 1. Results analogous to Mikolas theorem are the
defining property of these functions. A relationship between the Farey sequence
and the Riemann hypothesis other than the Franel-Landau theorem is postulated.
This conjecture involves a theorem of Mertens and the second Chebyshev
function.
