Sum of distinct divisors
Source: Canada 2002
March 5, 2006
number theory unsolvednumber theory
Problem Statement
Call a positive integer practical if every positive integer less than or equal to can be written as the sum of distinct divisors of .
For example, the divisors of 6 are 1, 2, 3, and 6. Since
\centerline{1={\bf 1}, ~~ 2={\bf 2}, ~~ 3={\bf 3}, ~~ 4={\bf 1}+{\bf 3}, ~~ 5={\bf 2}+ {\bf 3}, ~~ 6={\bf 6},}
we see that 6 is practical.
Prove that the product of two practical numbers is also practical.