MathDB

Inequality on sum of divisors of n - [IMO LongList 1971]

Source:

January 1, 2011

inequalitiesrationumber theory proposednumber theory

Problem Statement

Let us denote by

s(n)= \sum_{d|n} d

the sum of divisors of a positive integer

n

(

1

and

n

included). If

n

has at most

5

distinct prime divisors, prove that

s(n) < \frac{77}{16} n.

Also prove that there exists a natural number

n

for which

s(n) < \frac{76}{16} n

holds.