Has $F(n)=\prod\_{p\ {\rm prime}, p-1|n}p$ been studied?


This function interests me because for each prime $p$, the long-term average number of factors of $p$ in $n$ equals the long-term average number of factors of $p$ in $F(n)$.


Any non-trivial result would interest me, particularly the distribution of values of 
$\ln F(n)/\ln(n)$.



Has $F(n)=\prod_{p\ {\rm prime}, p-1|n}p$ been studied?
I think $F(n)$ is (more-or-less) the denominator of the Bernoulli number $B\_n$ by the Von Staudt–Clausen theorem, see <http://en.wikipedia.org/wiki/Von_Staudt>–Clausen\_theorem which refers you to <http://oeis.org/A002445>


