RADIUS OF CIRCLE

Totient maximum ¶ Euler's Totient function, φ( n ) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n . For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6. n Relatively Prime φ( n ) n /φ( n ) 2 1 1 2 3 1,2 2 1.5 4 1,3 2 2 5 1,2,3,4 4 1.25 6 1,5 2 3 7 1,2,3,4,5,6 6 1.1666... 8 1,3,5,7 4 2 9 1,2,4,5,7,8 6 1.5 10 1,3,7,9 4 2.5 It can be seen that n =6 produces a maximum n /φ( n ) for n ≤ 10. Find the value of n ≤ 1,000,000 for which n /φ( n ) is a maximum. As we know that to find the value of Euler Totient Function $\phi(n)$ we can use the following formula: $$\phi(n) = n\prod_{i = 1}^{k}\left(1 - \frac{1}{p^k}\right)$$ Where $p_1, p_2, p_3.....p_k$ are the prime factors of a given number $n$. But if we had to generate prime factors for each and every number using brute force method would increase