On the sum of distinct primes or squares of primes

In 1965 Erdős introduced f2(s): f2(s) is the smallest integer such that every l>f2(s) is the sum of s distinct primes or squares of primes where a prime and its square are not both used. We prove that for all sufficiently large s, f2(s)⩽p2+p3+⋯+ps+1+3106, and the set of s with the equality has the density 1.