  Let $A$ be a finite nonempty set of integers. An asymptotic estimate of
several dilates sum size was obtained by Bukh. The unique known exact bound
concerns the sum $|A+k\cdot A|,$ where $k$ is a prime and $|A|$ is large. In
its full generality, this bound is due to Cilleruelo, Serra and the first
author.
  Let $k$ be an odd prime and assume that $|A|>8k^{k}.$ A corollary to our main
result states that $|2\cdot A+k\cdot A|\ge (k+2)|A|-k^2-k+2.$ Notice that
$|2\cdot P+k\cdot P|=(k+2)|P|-2k,$ if $P$ is an arithmetic progression.
