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Re: prime powers < X

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  • Werner D. Sand
    ... up ... (1/5) ... That s allright. Can you sum it up into a closed form? WDS
    Message 1 of 2 , Dec 20, 2007
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      --- In primenumbers@yahoogroups.com, Kermit Rose <kermit@...> wrote:
      >
      >
      >
      >
      > 1. number of prime powers
      > Posted by: "Werner D. Sand" Theo.3.1415@... theo2357
      > Date: Tue Dec 18, 2007 4:00 pm ((PST))
      >
      > Who knows a good approximate formula for the number of prime powers
      up
      > to x (without simple prime numbers):
      > N = sum(1)(p^n <= x), p prime, n>1 ?
      >
      >
      > *******
      >
      >
      > Would this not be the number of primes < x
      > + the number of primes < x^(1/2)
      > + the number of primes < x^(1/3)
      > + the number of primes < x^(1/4)
      > + etc
      >
      >
      > approximately equal to
      >
      > [ x + 2 * x^(1/2) + 3 * x^(1/3) + 4 * x^(1/4) + 5 * x^
      (1/5)
      > + . . . ] / ln(x)
      >
      >
      >
      >
      > Kermit < kermit@... >


      That's allright. Can you sum it up into a closed form?
      WDS
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