Euler Totient, Revised

Define $\Phi(N)$ to be Euler's totient function, which is the number of positive integers $x$ in $0<x<N$ S.T. $GCD(x,N)=1$ . How many positive integers, in $1\leq y \leq 10^{3}$ , are not divisible by $2$ and satisfy the following?

$\Phi \left(\Phi \left(y\right)\right)=2^t \ , \ t \in \{1,2,3,\dots\}$