Let $P$ be a finite set of primes with $|P|\ge 2$ and let $\{a_1<a_2<\cdots \}=\{n\in \mathbb{N}:\text{if }p\mid n\text{ then }p\in P\}$. Is the sum$$\sum _{n=1}^{\infty }\frac{1}{[a_1,\dots ,a_n]},$$where $[a_1,\dots ,a_n]$ is the lowest common multiple of $a_1,\dots ,a_n$, irrational?

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

Let $P$ be a finite set of primes, (|P|\ge 2), and let (a_1<a_2<\cdots) be the increasing list of $P$-smooth numbers [[nomath]](i.e. all $n\in\mathbb N$ whose prime divisors lie in $P$)[[/nomath]]. Write [ L_n=[a_1,\dots,a_n]. ]

llm-hunter · gpt pro 5.2 · unverified

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