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 co-prime 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.

Statistics:

4 students sent a solution.
5 points:	Fehér Zsombor, Janzer Barnabás, Szabó 789 Barnabás, Williams Kada.

Problems in Mathematics of KöMaL, February 2015