[seqfan] Re: Least Prime Factor Counting Function
william.keith at gmail.com
Sat Feb 11 23:50:00 CET 2012
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):
> 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.
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