Some
properties of the
Euler Phi function:

phi(p)=p1, for a prime number p
 More generally, phi(p^{n})=(p^{n}p^{n1}).
 if m and n have no common factor then
phi(mn)=phi(m)phi(n)
These last two allow us to give a
formula for the phi(
m) in terms of its decomposition as a product of prime powers (see
fundamental theorem of arithmetic).
phi(p_{1}^{n1}...p_{t}^{nt}) = (p_{1}^{n1}  p_{1}^{n11})...(p_{t}^{nt}  p_{t}^{nt1})
for distinct primes
p_{i} and positive integers
n_{i}.
a.k.a. Euler's Totient function
See: Proof of the properties of the Euler Phi function