[seqfan] Re: Least Prime Factor Counting Function
william.keith at gmail.com
Sat Feb 11 12:42:09 CET 2012
The number 7 will be the smallest prime factor of every 7th number that is
not divisible by 2, 3, or 5. Thus the number of 7s in the list of smallest
prime factors of numbers in an interval from x to x+c will be periodic with
period 210 (2*3*5*7), with a different function for each c. Since the
periods for each prime are subperiods of the periods for larger primes, the
correlations over large intervals will be very strong.
I'm not sure what you want concerning telescoping series. The fraction
will be roughly a product of 1/(2*3*5*7) times c, with fractional
corrections based on your starting point x.
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