[seqfan] Re: Least Prime Factor Counting Function

[William Keith]

On Sat, Feb 11, 2012 at 2:03 PM, fransis fransis <fransisf at gmail.com> wrote:

> Hi, I noticed that the number of 7s in the list of smallest
> prime factors of numbers is exactly 1/6 of the total of the values greater
> than 7
> in a periodic fashion.
>
> For exactly this arguments of the lpf(i):
>
> 30,53,54,55,56,57,58,79,80,81,82,107,108,187,188,189,190,211,212,213,214,215,216,239
> the ratio is 1/6.
> And it seems so for 30+ k210,53+k210,........,239+k210
> So is it possible that this is true for all primes,id est Pi(p)/Pi(>p)==
> 1/(p-1) for a fixed number of arguments of lpf and a period Prod(i<p)?.
>

If by that last product you mean the product of all primes less than p,
that is indeed correct.  The number of arguments for which it holds will
also be a simple function of the prime you are looking at.

William Keith