Some properties of the Euler Phi function:
  • phi(p)=p-1, for a prime number p
  • More generally, phi(pn)=(pn-pn-1).
  • 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(p1n1...ptnt) = (p1n1 - p1n1-1)...(ptnt - ptnt-1)
for distinct primes pi and positive integers ni.

a.k.a. Euler's Totient function

See: Proof of the properties of the Euler Phi function

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