The Euler indicatrix : euler phi

### 5.6.25 The Euler indicatrix : euler phi

euler (or phi) returns the Euler indicatrix for a integer.
euler(n) (or phi(n)) is equal to the number of integers less than n and prime with n.
Input :

euler(21)

Output :

12

In other words E={2,4,5,7,8,10,11,13,15,16,17,19} is the set of integers less than 21 and coprime with 21. There are 12 members in this set, hence Cardinal(E)=12.

Euler has introduced this function to generalize the little Fermat theorem:

If a and n are mutually prime then aeuler(n)=1 mod n