Any Relationship?

[Lokolo]

Doing maths cousework, Phi Function and i came out with these numbers (i dnt no if it has anything do to with phi number yet)

i) Φ (4²) = Φ(16) = 2
ii) Φ (6²) = Φ(36) = 12
iii) Φ (8²) = Φ(64) = 32

its looks as if there could b a relatonship between them but i cant see one, can you?
thanks

Lokolo

[Muzza]

phi(16) != 2, since 1, 3, 5, 7, 9, 11, 13 and 15 are all coprime to 16. phi(16) = 8.

[Lokolo]

opps yeh sorry, so do you think there will be a general forumla? i have got one for prime squares
Φ(p²) = p² - p
where p = prime
but not one for all others

[Muzza]

Well... phi(ab) = phi(a)phi(b) if a and b are relatively prime, and phi(p^n) = p^n - p^(n - 1) where p is a prime and n a natural number. Those are the ones I know of. And of course, those two formulas taken together provide an easy way to compute phi(x) if you know the prime factorization of x.

[Lokolo]

wow, i have a lot of testin to do....
thanks muzza