User blog comment:Primussupremus/Extended busy beaver or super sigma./@comment-29915175-20170406195949/@comment-30754445-20170406201842

"This is just an iterated Busy Beaver function"

Yup.

And since "interating a function" is equivalent to adding 1 to the function's FGH ordinal, the strength of this one is ωck +1. :-)