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 A072613 Number of numbers of the form p*q (p, q distinct primes) less than or equal to n. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 COMMENTS 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 Number of squarefree semiprimes not exceeding n. - Wesley Ivan Hurt, May 25 2015 REFERENCES G. Tenenbaum. Introduction to Analytic and Probabilistic Number Theory. (Cambridge Studies in Advanced Mathematics 1995.) LINKS N. J. A. Sloane, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Semiprime. FORMULA a(n) = Sum_{p= 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 MATHEMATICA fPi[n_] := Sum[ PrimePi[n/ Prime@i] - i, {i, PrimePi@ Sqrt@ n}]; Array[ fPi, 81] (* Robert G. Wilson v, Jul 22 2008 *) Accumulate[Table[If[PrimeOmega[n] MoebiusMu[n]^2 == 2, 1, 0], {n, 100}]] (* Wesley Ivan Hurt, Jun 01 2017 *) Accumulate[Table[If[SquareFreeQ[n]&&PrimeOmega[n]==2, 1, 0], {n, 100}]] (* Harvey P. Dale, Aug 05 2019 *) PROG (PARI) a(n)=sum(k=1, n, if(abs(omega(k)-2)+(1-issquarefree(k)), 0, 1)) (PARI) a(n) = my(t=0, i=0); forprime(p = 2, sqrtint(n), i++; t+=primepi(n\p)); t-binomial(i+1, 2) \\ David A. Corneth, Jun 02 2017 (PARI) upto(n) = {my(l=List(), res=[0, 0, 0, 0, 0], j=1, t=0); forprime(p = 2, n, forprime(q=nextprime(p+1), n\p, listput(l, p*q))); listsort(l); for(i=2, #l, t++; res=concat(res, vector(l[i]-l[i-1], j, t))); res} \\ David A. Corneth, Jun 02 2017 CROSSREFS Cf. A072000. Sequence in context: A243283 A243284 A338623 * A029551 A171482 A132015 Adjacent sequences:  A072610 A072611 A072612 * A072614 A072615 A072616 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Aug 11 2002 STATUS approved

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Last modified September 20 10:18 EDT 2021. Contains 347584 sequences. (Running on oeis4.)