## Could I apply the master theorem if my $N/b$ is $\varphi(N)$?

Let

$$T(N) = \begin{cases}1 & \text{if } N = 1\ T(\varphi(N)) + \log(\varphi(N))^3 & \text{otherwise} \end{cases}$$

Can I somehow express $$\varphi(N)$$ as $$N/b$$, so I can apply the Master Theorem and resolve this recurrence?