You are referring to circumvention of roadblocks.
This is a different kind of problem.
end game:
Suppose that N is coprime to 3*5*7*11*13*31.
Give a lower bound on N.
circumvention of roadblock:
Suppose N < 10^2100.
Suppose that N is coprime to 127*19.
Suppose that 7^378  N and that no prime factor of sigma(7^378).
Give an upper bound on the smallest prime divisor of N distinct from 7.
I will update the section about circumventing roadblocks
since the factors of sigma(2801^82) are now known and I will add more explanations
for you to see where the numbers come from.
