  The Riemann hypothesis is equivalent to the Li criterion governing a sequence
of real constants, that are certain logarithmic derivatives of the Riemann xi
function evaluated at unity. We investigate a related set of constants c_n, n =
1,2,..., showing in detail that the leading behaviour (1/2) ln n of lambda_n/n
is absent in c_n. Additional results are presented, including a novel explicit
representation of c_n in terms of the Stieltjes constants gamma_j. We
conjecture as to the large-n behaviour of c_n. Should this conjecture hold,
validity of the Riemann hypothesis would follow.
