More complex integers In connection to this question:
Expected values of Kolmogorov complexity in a random sample

Let $n$ be number of bits. Let $A = \{0,1,2,\dots,2^{n}-1\}$ be indexed by the $n$-bits. Let $ \delta &gt; 0$ be fixed. Is there an estimate of what fraction of integers in $A$ can have Kolmogorov complexity be greater than $\delta n$?
The argument is the same, there are only $1 + 2 + 4 + ... + 2^{\delta n - 1}$ programs shorter than $\delta n$ so there are at least $2^n - (2^{\delta n} - 1)$ integers with $K(x) \geq \delta n$.