Let \(a(n)\) be the number of unordered factorizations of \(n\) into divisors larger than \(1\). Prove that \(\sum_{n=2}^{\infty} \frac{a(n)}{n^2} = 1\).

The best solution was submitted by 김기수 (KAIST 수리과학과 18학번, +4). Congratulations!

Here is the best solution of problem 2022-18.

Other solutions were submitted by 기영인 (KAIST 22학번, +3), Kawano Ren (Kaisei Senior High School, +3), Sakae Fujimoto (Osaka Prefectural Kitano High School, Freshmen, +3), 최백규 (KAIST 생명과학과 20학번, +3).