I'm trying to solve the following problem $:$
Define $T(2^n) = T(2^n/n) + 1$ with $T(1) = 1$ . Is $T(2^n)∈ Θ(n) ?$
If I convert this recurrence relation into $:$
Define $T(k) = T(k/log_2k) + 1$ with $T(2) = 1$ . Is $T(k)∈ Θ(log_2k) ?$ with assumption $k = 2^n$
Since if $T(n)=aT(n/b)+f(n),$ it would be of order $Θ(logn),$ if $a==1$ and $f(n)==1.$ Using master theorem $,$ I'm guessing $.$
Can you explain in formal way, please?