Let P(x,d,a) denote the number of primes p<=x with p=a(mod d). Chebyshev's bias is the phenomenon that `more often' P(x;d,n)>P(x;d,r),
than the other way around, where n is a quadratic non-residue mod d and r is a quadratic residue mod d. If P(x;d,n)>=P(x;d,r)
for every x up to some large number, then one expects that N(x;d,n)>=N(x;d,r) for every x. Here N(x;d,a) denotes the number
of integers n<=x such that every prime divisor p of n satisfies p=a(mod d). In this paper we develop some tools to deal
with this type of problem and apply them to show that, for example, N(x;4,3)>=N(x;4,1) for every x.In the process we express
the so called second order Landau-Ramanujan constant as an infinite series and show that the same type of formula holds true
for a much larger class of constants.

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