Let p(i) denote the i-th prime number. (Thus (p1, p2, p3,....) = (2, 3, 5, ... ).)

Find the smallest positive integer k such that the product n = p1 p2 ... pk satisfies

s(n) > 3n. Is there any positive integer m < n satisfying s(m) > 3m?

s denotes the sum of divisors function.

Honestly I have 0 clue on how do I start a question like this...

It would be nice, if someone can lead me to the right way.

Thanks