The prime-power plus almost-prime conjecture

Let $k\geq 1$ be odd, and let $N$ be a sufficiently large even number. Prime-power plus almost-prime conjecture. Then $N$ can be expressed as the sum of a $k$th power of a prime and a number with at most $k$ prime factors. This is presented as a particularly neat consequence of the conjectural value $\widetilde{M}(k)=k$; no resolution is given.