We study the distribution of a family of generalized Euler constants arising from integers sieved by finite sets of primes . For , the set of the first r primes, as r → ∞. Calculations suggest that is monotonic in r, but we prove it is not. Also, we show a connection between the distribution of and the Riemann hypothesis.
(Received March 19 2007)
(Revised July 07 2007)
† Research of the second author supported by National Science Foundation grant DMS-0555367.