# Reference request for proof of Landau's generalised PNT

Could someone please point me in the direction of a proof for Landau's asymptotic formula for k-almost primes:

$$\pi_k(n) \sim \left( \frac{n}{\log n} \right) \frac{(\log\log n)^{k-1}}{(k - 1)!}$$

I realise that it was derived directly from the PNT - would like to see the steps involved though.

• I'm not sure, but it might be in Davenport's Multiplicative Number Theory. – Gerry Myerson Jan 2 '14 at 18:51
• @martin: ALso, have you checked the reference here? en.wikipedia.org/wiki/Almost_prime, that is: ^ Tenenbaum, Gerald (1995). Introduction to Analytic and Probabilistic Number Theory. Cambridge University Press. ISBN 0-521-41261-7. – Amzoti Jan 2 '14 at 18:58
• Thanks for the suggestions - can't seem to find it in Davenport though - do you have a chapter ref? – martin Jan 2 '14 at 19:17
• See also the discussion at mathoverflow.net/questions/35927/… – Gerry Myerson Jan 3 '14 at 1:09
• I note that just a couple of weeks ago, you claimed to have a better formula than Landau's; math.stackexchange.com/questions/607895/… – Gerry Myerson Jan 3 '14 at 1:13