σ(n)Φ(n)≥n^2(1-1/p1^2)(1-1/p2^2)...(1-1/pr^2)
I can show that
σ(n)Φ(n)≥n^2(1-1/p1)(1-1/p2)...(1-1/pr)
but am unsure of how to do it with the pi^2.
I think it'd be a good idea if you defined what you use: what's that sigma function: the sum of all the divisors of the number n? And those p_i's are the prime divisors of n? If so the claim is false:
By the way, without the squares we get equality with n = 6.
Tonio