For a prime power $p^a$ define $\gamma(p^a) := (p^a-1)(p^{a-1}-1)\cdots(p^{2}-1)(p-1)$,
  For a natural number $n$, if $n = \prod {p_{i}}^{\alpha_{i}}$ where $p_1,\dots,p_k$ are
 distinct prime numbers, define $\gamma(n) := \prod \gamma({p_{i}}^{\alpha_{i}}) $.
 
 
If $p$ is  a  <a href="http://en.wikipedia.org/wiki/Zsigmondy%27s_theorem">primitive prime divisor</a> of $2^{8n+4} - 1 $, can we get that $ p \nmid \gamma(\dfrac{2^{8n+4} - 1}{2^{2n+1} + 1}) $?