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Well known property of sigma(n)

Source: India tst 2002 p8

July 13, 2012
number theory proposednumber theory

Problem Statement

Let σ(n)=∑d∣nd\sigma(n)=\sum_{d|n} d, the sum of positive divisors of an integer n>0n>0.
(a) Show that σ(mn)=σ(m)σ(n)\sigma(mn)=\sigma(m)\sigma(n) for positive integers mm and nn with gcd(m,n)=1gcd(m,n)=1
(b) Find all positive integers nn such that σ(n)\sigma(n) is a power of 22.
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