Let $s_t(n)$ be the $t$-smooth component of $n$ - that is, the product of all primes $p$ (with multiplicity) dividing $n$ such that $p<t$. Let $f(n,t)$ count the number of distinct possible values for $s_t(m)$ for $m\in [n+1,n+t]$. Is it true that$$f(n,t)\gg t$$(uniformly, for all $t$ and $n$)?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

As far as I can tell from the literature that’s easy to locate, this is **still open** in the fully uniform form you stated.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.