multiple of perfect number is abundant

Quote:

A positive integer n is abundant if sigma(n) > 2n (where sigma(n) = sum of divisors of n)

An integer k is prefect if sigma(k) = 2k

I need to prove that a multiple of a perfect number is abundant.

Suppose **n** is a prefect number and **k** is a nonnegative integer.

If gcd(n,k)=1 then sigma(nk) = sigma(n) * sigma(k) = 2n * sigma(k) > 2nk

Otherwise... this is where I'm having some trouble.. any suggestions?

Re: multiple of perfect number is abundant

I arrived at the solution. It was much simpler than what I attempted in the original post.

Re: multiple of perfect number is abundant