Is there a relationship between these numbers from the Phi function?

In summary, the conversation discusses the use of the Phi function in mathematics coursework and its relation to certain numbers. The speaker mentions specific examples, such as Φ(4²) = 2, and questions if there is a general formula for all numbers. Another person responds with two known formulas for the Phi function and suggests using the prime factorization of a number to compute phi(x). The original speaker expresses appreciation and plans to conduct further testing.
  • #1
Lokolo
10
0
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 can't see one, can you?
thanks

Lokolo
 
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  • #2
phi(16) != 2, since 1, 3, 5, 7, 9, 11, 13 and 15 are all coprime to 16. phi(16) = 8.
 
  • #3
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
 
  • #4
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.
 
Last edited:
  • #5
wow, i have a lot of testin to do...
thanks muzza
 

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