Let be the sum of all divisors of . See sum-of-divisors function definition in https://en.wikipedia.org/wiki/Divisor_function.
Solve .
The answers are .
What are the strategies for solving this equation?
I can see that since , but there are too many factorizations of to try.
The method in my lecture notes is only suitable for small numbers on the RHS of the equation.
Write down the values of for primes and integers , stop when the the value is greater than meaning it cannot be a factor or .
: 3,7,15,31,...
: 4,13,40,...
: 6,31,156,...
: 8,57,...
: 12,133,...
: 14,183,...
: 18,...
: 20,...
: 24,...
:
: 48,...
Identify the ones that are factors of .
, , , , , .
Then
and so ;
and so ;
and so .