What are the chances that, for an arbitrary $p$-local harmonic spectrum $X$, if $K(n)\wedge X\simeq\ast$ for all $n$, then $X$ is contractible? This, I believe, holds for suspension spectra and finite spectra. Does anyone know of any harmonic (i.e. local to $\vee_{n\in\mathbb{N}}K(n)$) spectra for which this does not hold?

Thanks!