20100816, 20:12  #1 
Aug 2006
5,987 Posts 
Asymptotic density of kalmost primes
Of course this is
for any fixed k, but are there better Litype estimates, or at least more asymptotic terms (as Cipolla 1902 gives for )? For extra points:
This comes out of comparing the number of nbit semiprimes to the number predicted by the formula with k = 2, where I noticed what seemed to be a consistent relative (reciprocal density) bias of about 0.5 over the range 1550 bits. 
20100822, 23:47  #2 
"William"
May 2003
Near Grandkid
2×1,187 Posts 
You might try an Li version motivated by comparison to the prime case. When k=1 this is n/log(n), which we know to improved upon by integral (1/log(x)). This can be motivated by the argument that 1/log(x) is correct density. The analogous adjustment would be the integral of

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