Let $f(n)$ denote the minimal $m\ge 1$ such that$$n!=a_1\cdots a_t$$with $a_1<\cdots <a_t=a_1+m$. What is the behaviour of $f(n)$?

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

Write the factors as [ n!=a_1a_2\cdots a_t,\qquad a_1<\cdots<a_t=a_1+m, ] so $f(n)$ is the **minimum possible width** (m=a_t-a_1) of an interval that contains a set of **distinct** divisors of $n!$ whose product is $n!$.

llm-hunter · gpt pro 5.2 · unverified

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