{"schema":"vela.problem-packet.v0.1","problem":912,"statement":"If\\[n! = \\prod_i p_i^{k_i}\\]is the factorisation into distinct primes then let $h(n)$ count the number of distinct exponents $k_i$. Prove that there exists some $c>0$ such that\\[h(n) \\sim c \\left(\\frac{n}{\\log n}\\right)^{1/2}\\]as $n\\to \\infty$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[{"id":"A071626","name":"Number of distinct exponents in the prime factorization of n!.","terms":"0,1,1,2,2,3,3,3,3,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,","url":"https://oeis.org/A071626"}],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}