Let L: [1, ∞) → [1, ∞) be a nondecreasing function such that limx→∞L(x) = +∞. Let f= fL be a strongly additive function determined by f(p) = L(p) on the set of primes. In what followsp, p1, p2, …, q, q1, q2, …,P, Q stand for prime numbers, P(n) denotes the largest prime divisor of n. The letters c, c1, c2, … denote suitable positive constants, not necessarily the same at each occurrence. As usual, π(x) denotes the number of primes p ≤ x, while π(x, k, ℓ) is the number of primes p ≤ x such that p ≡ ℓ (mod k).