title: "IMO 1971 LL AUT2" description: "Let us denote by s(n) = " date: "2026-05-29T11:51:44+07:00" tags: ["imo", "longlist", "mathematics", "olympiad"] categories: ["mathematics"] year: 1971 type: "longlist" origin: "AUT" weight: 197100002 draft: false

IMO 1971 LL AUT2

Origin: AUT

Problem

Let us denote by s(n) =  d|n d the sum of divisors of a natural number n (1 and n included). If n has at most 5 distinct prime divisors, prove that s(n) < 77 16n. Also prove that there exists a natural number n for which s(n) > 76 16n holds.