

How (not) to compute harmonic numbers (2009) - nkurz
http://fredrik-j.blogspot.com/2009/02/how-not-to-compute-harmonic-numbers.html

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tzs
Speaking of the harmonic numbers, there is an interesting conjecture. Let H_n
be the n'th harmonic number. Let s(n) by the sum of the positive divisors of
n. For example s(6) = 1 + 2 + 3 + 6. Then it is conjectured that:

    
    
       s(n) <= H_n + exp(H_n) log(H_n)
    

with equality only in the case n = 1.

What is interesting about this conjecture is that it is true if and only if
the Riemann Hypotheses is true! [1]

The Riemann Hypothesis is one of, if not the, most important unresolved issues
in mathematics.

[1]
[http://xxx.lanl.gov/abs/math.NT/0008177/](http://xxx.lanl.gov/abs/math.NT/0008177/)

