Problem Teachers' Notes Hint Solution

Black Box

The functions are

1. nth Prime number $P(n)$
2. $\Phi(n)$ (Euler's totient function) -- the number of numbers less than n which are coprime to n. For example $\Phi(22) = 10, \Phi(6) = 2$.
3. Prime counting function $\Pi(n)$ -- the number of primes less than or equal to $n$. For example, $\Pi(10)= 4, \Pi(23) = 9$.
4. The number of divisors of the number.
5. The nth digit of $\pi$.