MathDB

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Part of 1971 IMO Longlists

Problems(1)

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

Source:

1/1/2011
Let us denote by s(n)=∑d∣nds(n)= \sum_{d|n} d the sum of divisors of a positive integer nn (11 and nn included). If nn has at most 55 distinct prime divisors, prove that s(n)<7716n.s(n) < \frac{77}{16} n. Also prove that there exists a natural number nn for which s(n)<7616ns(n) < \frac{76}{16} n holds.
inequalitiesrationumber theory proposednumber theory