# Functional Number Theoretic Function

Let $$f (x)$$ be a function on $$x$$ which satisfies following conditions:

$\begin{cases} f (\phi (x)+3) \leq f (x+3) +7 \\ f (x+1) \geq f (\phi (x)) \\ f (2)=7 \end{cases}$

Find the value of $$f (4)+f (5)+15$$.

Notation: $$\phi(\cdot)$$ denotes the Euler's totient function.

×