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number of prime powers

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  • Werner D. Sand
    Who knows a good approximate formula for the number of prime powers up to x (without simple prime numbers): N = sum(1)(p^n 1 ? Suggestion:
    Message 1 of 1 , Dec 18, 2007
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      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 ?

      Suggestion: N ~ sqrt(x ln x) / ((ln ln x)^(ln ln x))

      Hardy's formula (1999) N ~ sqrt(x)*ln(x) is only an upper bound and not
      what I am looking for.

      Werner D. Sand
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