• If
P(
n) is the largest
prime factor of
n, then \liminf P(n)/\log n=1. • P(n)\ll \log^\delta n holds for an exponent \delta=37/20. • It is conjectured that \limsup P(n) / \log n = 2. • They are always even because if x is odd, then 2x also has the same Totient function, trivially failing the condition that all numbers more than it has more value of Totient function than it. ==References==