A Kubilius model for sieve-theoretic sequences

We bound the total variation distance in the Kubilius model for sequences with positive level of distribution. We obtain a result that we expect is qualitatively optimal. As a special case, it recovers a recent result of Ford on shifted primes, with a slightly simplified proof. In the classical case considered by Kubilius, our theorem gives a simple proof of the optimal bound discovered by Tenenbaum, up to factors of xᵒ⁽¹⁾ x o ( 1 ) and uᵒ⁽ᵘ⁾ u o ( u ) .