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A072613
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Number of numbers of the form p*q (p, q distinct primes) less than or equal to n.
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3
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0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 9, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 22, 22
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OFFSET
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1,10
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COMMENTS
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There was an old comment here that said a(n) was equal to A070548(n) - 1, but this is false (e.g. at n=210). - N. J. A. Sloane, Sep 10 2008
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REFERENCES
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G. Tenenbaum. Introduction to Analytic and Probabilistic Number Theory. (Cambridge Studies in Advanced Mathematics 1995).
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 1..10000
Weisstein, Eric W., Semiprime.
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FORMULA
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a(n)=\sum_{p<sqrt(n)}(Pi(x/p)-Pi(p)), where Pi(n) is the prime counting function, A000720, and the sum is over all primes less than sqrt(n). [N-E. Fahssi, Mar 05 2009]
Asymptotically a(n)~ (n/Log(n))Log(Log(n)) [G. Tenenbaum pp 200--].
a(n) = sum( mu(i) * floor(Omega(i)/2) * floor(2/Omega(i)), i = 1..n ). - Wesley Ivan Hurt, Jan 05 2013
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EXAMPLE
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a(6) = 1 since 2*3 is the only number of the form p*q less than or equal to 6.
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MAPLE
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f:=proc(n) local c, i, j, p, q; c:=0; for i from 1 to n do p:=ithprime(i); if p^2 >= n then break; fi; for j from i+1 to n do q:=ithprime(j); if p*q > n then break; fi; c:=c+1; od: od; RETURN(c); end; - N. J. A. Sloane, Sep 10 2008
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MATHEMATICA
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fPi[n_] := Sum[ PrimePi[n/ Prime@i] - i, {i, PrimePi@ Sqrt@ n}]; Array[ fPi, 81] (* Robert G. Wilson v, Jul 22 2008 *)
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PROG
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(PARI) a(n)=sum(k=1, n, if(abs(omega(k)-2)+(1-issquarefree(k)), 0, 1))
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CROSSREFS
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Cf. A072000.
Sequence in context: A069623 A076411 A217038 * A029551 A171482 A132015
Adjacent sequences: A072610 A072611 A072612 * A072614 A072615 A072616
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre, Aug 11 2002
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STATUS
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approved
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