MathDB

For every positive integer

n

let

\sigma(n)

denote the sum of all its positive divisors. A number

n

is called weird if

\sigma(n)\ge2n

and there exists no representation

n=d_1+d_2+\ldots+d_r,

where

r>1

and

d_1,\ldots,d_r

are pairwise distinct positive divisors of

n

. Prove that there are infinitely many weird numbers.

Problem Statement