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Question about A052130

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  • asposer
    Sloane s A052130 is generated as follows: a(n) = number of numbers between 1 and 2^m with m-n prime factors (counted with multiplicity). . . . a(n) = number of
    Message 1 of 1 , Mar 24 3:43 PM
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      Sloane's A052130 is generated as follows:

      a(n) = number of numbers between 1 and 2^m with m-n prime
      factors (counted with multiplicity). . . .

      a(n) = number of products of half-odd-primes <= 2^n. E.g. a(2) = 7
      since 1, 3/2, (3/2)^2, (3/2)^3, (3/2)*(5/2), 5/2, 7/2 are all <= 2^2

      I'm curious as to why this is the case; i.e., why the number of
      integers with m-n prime factors would be equal to then number of half-
      odd-primes <= 2^n. Again, my Google skills have failed me in looking
      for an answer. Could someone point me in the right direction?
      Thanks!

      -Andrew-


      Here's the full link to the sequence from the online integer database:

      http://www.research.att.com/cgi-
      bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A052130
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