MathDB

For every positive integer

n

, let

\sigma(n)

denote the sum of all positive divisors of

n

(

1

and

n

, inclusive). Show that a positive integer

n

, which has at most two distinct prime factors, satisfies the condition

\sigma(n)=2n-2

if and only if

n=2^k(2^{k+1}+1)

, where

k

is a non-negative integer and

2^{k+1}+1

is prime.

Problem Statement