{"schema":"vela.problem-packet.v0.1","problem":690,"statement":"Let $d_k(p)$ be the density of those integers whose $k$th smallest prime factor is $p$ (i.e. if $p_1<p_2<\\cdots$ are the primes dividing $n$ then $p_k=p$).For fixed $k\\geq 1$ is $d_k(p)$ unimodular in $p$? That is, it first increases in $p$ until its maximum then decreases.","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}