1. Let d(n) denote the number of positive integers that divide n, including 1 and n. For example, d(1)=1, d(2)=2, and d(12)=6. (This function is known as the divisor function.) Let f(n)=d(n)/∛n. There is an integer number N which makes f(N)=max(f(n)). What is N?
2. Semicircle Γ has diameter AB of length 14. Circle Ω lies tangent to AB at point P and intersects Γ at points Q and R. If QR=3√3 and ∠QPR=60°, What is the area of ΔPQR in the form of a√b/c?