On the equation 4n = 1x + 1y + 1z

It is proved that for any given positive integers N and k the number of integers n < N for which the equation $\text{4}\text{n}\text{=}\text{1}\text{x}\text{+}\text{1}\text{y}\text{+}\text{1}\text{z}$ is unsolvable in positive integers x, y, z is not greater than $\text{cN}\text{(}\text{log}\text{N)}{}^{\mathrm{k}}$, where c is a constant depending only on k.