« Vrati se
Let n be a positive integer. Let \sigma(n) be the sum of the natural divisors d of n (including 1 and n). We say that an integer m \geq 1 is superabundant (P.Erdos, 1944) if \forall k \in  \{1, 2, \dots , m - 1 \}, \frac{\sigma(m)}{m} >\frac{\sigma(k)}{k}.
Prove that there exists an infinity of superabundant numbers.

Slični zadaci

#NaslovOznakeRj.KvalitetaTežina
1611IMO Shortlist 1983 problem 150
1606IMO Shortlist 1983 problem 100
1602IMO Shortlist 1983 problem 60
1355IMO Shortlist 1969 problem 250
1354IMO Shortlist 1969 problem 240
1353IMO Shortlist 1969 problem 230