Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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