# Little-o vs. asymptotic equivalence

As big- and little-o notation are a little too technical to me, I prefer an expression with asymptotic equivalence ($\sim$). However, how does one "translate" this expression to an asymptotic equivalence? It's about the primorials, as found on Wikipedia (http://en.wikipedia.org/wiki/Primorial).

$p_n\#=e^{(1+o(1))\cdot n\cdot\log{n}}$

Is it possible to express this using $\sim$-notation?
Help is greatly appreciated.

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You can't, at least not directly, since we have $e^{n\cdot\log{n}}\nsim e^{(1+1/n)\cdot n\cdot\log{n}}=e^{n\cdot\log{n}}\cdot n$.
You can say something like $\log(p_n\#)\sim n\cdot\log{n}$, though.