  A group of infinite products over low-order rational polynomials evaluated at
the sequence of prime numbers is loosely called the Hardy-Littlewood constants.
In this manuscript we look at them as factors embedded in a super-product over
primes, semiprimes, 3-almost primes etc. Numerical tables are derived by
transformation into series over k-almost prime zeta functions. Alternative
product representations in a basis of k-almost prime products associated with
Euler's formula for the Riemann zeta function are also pointed out.
