Erdős Problem #462

declared status 'open'. Formalized: no. Let $p(n)$ denote the least prime factor of $n$. There is a constant $c>0$ such that$$\sum_{\substack{n<x\\ n\textrm{ not prime}}}\frac{p(n)}{n}\sim c\frac{x^{1/2}}{(\log x)^2}.$$Is it true that there exists a constant $C>0$ such that$$\sum_{x\leq n\leq x+Cx^{1/2}(\log x)^2}\frac{p(n)}{n} \gg 1$$for all large $x$? Prize: no. OEIS: A032742. Tags: number theory, primes.

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