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#1 |
Aug 2006
5,987 Posts |
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Of course this is
for any fixed k, but are there better Li-type estimates, or at least more asymptotic terms (as Cipolla 1902 gives for For extra points:
This comes out of comparing the number of n-bit 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 15-50 bits. |
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#2 |
"William"
May 2003
Near Grandkid
2×1,187 Posts |
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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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