Decide for which positive values on a that makes the series converge

For which positive values on a does the series converge?:

$$\sum _{n=1}^{\infty}na^{\ln(n)}$$

I have tried to rewrite the expression, but that gives me nothing.

Anyone got a clue?

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I will guess that your $i$ should be an $n$. If $a$ is positive, we may write it as $e^x$ for some $x$. Then $$na^{\ln(n)}=n(e^x)^{\ln(n)}=ne^{\ln(n^x)}=n(n^x)=n^{x+1}.$$ Now you've got yourself a $p$-series.
Yep, changed that. But why can you change a to $$e^x$$ ? –  Curtain Dec 10 '12 at 22:04
@JulianAssange $x = \ln(a)$ –  Tom Oldfield Dec 10 '12 at 22:25