Jeffrey Lagarias proved, unconditionally, that: $$ \sigma(n)<H_n+2\exp(H_n)\log(H_n)\qquad n>1 $$

This was posed as a problem in:

- J. C. Lagarias,
*Problem 10949: A generous bound for divisor sums*, American Math. Monthly**109**no 6 (2002) 569, doi:10.2307/2695448

(**edit:** with solution given in AMM **111** no 3 (2004), 264–265, doi:10.2307/4145148)

Where can I find this problem? Or, any other links that shows how the inequality has been derived would be greatly appreciated.

EDIT: I will also accept the answer if anyone can outline the steps, how Lagarias derived his criterion.

alsoproved unconditionally …" in the first sentence of your question? $\endgroup$ – LSpice Oct 13 at 22:39