Today I resolved this kata on Shell and I'm thirteenth... :)
Oooooh!!!
It is rather difficult task for Shell/Bash.
The key stone is Perfomance!!!
One day for writing code and one week for it's optimisation.
For success it is necessary to understand math theory:

• square properties,
• division algorithms,
• factorization,
• square root properties and finding algorithms,
• prime numbers.
  Carefull reading articles on Wikipedia will be enought.

Also Shell things like: loops, logical conditions, arithmetic module and a lot of small but important nuances. For example ((i+=1)) faster then i=$((i+1))

For optimisation very helpful Math theory and understanding how Shell works - avoiding sub-shell inside loops, pipes and non-builtin programs - their are make code slower.
Even after several years of expirience I discovered a lot of new things for me, like custom PS4 and 'factor'.

P.S. Author, thank You for this kata. Sometimes during deeep optimisation I was hated You! :) but finally I'm thankful! :))