Problem A. 635. (February 2015)
A. 635. Show that for every positive real number \(\displaystyle c>0\) there is a positive integer \(\displaystyle n\) such that \(\displaystyle \varphi\big(\sigma(n)\big)>cn\). (For an arbitrary postive integer \(\displaystyle k\), \(\displaystyle \varphi(k)\) denotes the number of positive integers not exceeding \(\displaystyle k\) that are coprime with \(\displaystyle k\). \(\displaystyle \sigma(k)\) is the sum of positive divisors of \(\displaystyle k\).)
Proposed by: Barnabás Szabó, Budapest
(5 pont)
Deadline expired on March 10, 2015.
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