%I A072000
%S A072000 0,0,0,1,1,2,2,2,3,4,4,4,4,5,6,6,6,6,6,6,7,8,8,8,9,10,10,10,10,10,10,10,
%T A072000 11,12,13,13,13,14,15,15,15,15,15,15,15,16,16,16,17,17,18,18,18,18,19,
%U A072000 19,20,21,21,21,21,22,22,22,23,23,23,23,24,24,24,24,24,25,25,25,26
%N A072000 Number of semiprimes (A001358) <= n.
%C A072000 Number of k <= n such that bigomega(k) = 2.
%D A072000 A. Hildebrand, On the number of prime factors of an integer, in Ramanujan 
               Revisited (Urbana-Champaign, Ill., 1987), pp. 167-185, Academic Press, 
               Boston, MA, 1988.
%D A072000 E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, vol. 
               1, Teubner, Leipzig, 1909; third edition : Chelsea, New York (1974).
%D A072000 G. Tenenbaum, Introduction \`a la th\'eorie analytique et probabiliste 
               des nombres, p. 203, Publications de l'Institut Cartan, 1990.
%H A072000 Daniel Forgues, <a href="b072000.txt">Table of n, a(n) for n=1..40882</
               a>
%H A072000 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Semiprime.html">Semiprime</a>
%F A072000 Let Pi(x) denote the number of primes <= x (cf. A000720). Then 2*a(n) 
               = Sum_{ primes p <= n/2 } Pi(n/p) + Pi(sqrt(n)). [Landau, p. 211]
%F A072000 Let Pi(x) denote the number of primes <= x (cf. A000720). Then a(n) = 
               Sum_{i=1..Pi(sqrt(n))} (Pi(n/prime(i)) - i + 1). - Robert G. Wilson 
               v Feb 07 2006
%F A072000 a(n) = card{ x <= n : bigomega(x) = 2 }.
%F A072000 Asymptotically a(n) ~ n*loglog(n)/log(n). [Landau, p. 211]
%F A072000 Let A be a positive integer. Then card{ x <= n : bigomega(x) = A } ~ 
               (n/log(n))*log(log(n))^(A-1)/(A-1)! [Landau, p. 211]
%F A072000 a(n) = A072613(n)+A056811(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 10 2007
%F A072000 a(n) = SUM[i=1..n] A064911(i). - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Dec 30 2007
%p A072000 A072000 := proc(n) local sp,t ; sp := 0 ; for t from 1 to n do if numtheory[bigomega](t) 
               = 2 then sp := sp+1 ; fi ; od ; sp ; end: for n from 1 to 180 do 
               printf("%d, ",A072000(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 10 2007
%t A072000 SemiPrimePi[n_] := Sum[ PrimePi[n/Prime@i] -i + 1, {i, PrimePi@Sqrt@n}]; 
               Array[SemiPrimePi, 78] (from Robert G. Wilson v (rgwv(at)rgwv.com), 
               Jan 03 2006)
%o A072000 (PARI) for(n=1,100,print1(sum(i=1,n,if(bigomega(i)-2,0,1)),","))
%Y A072000 Cf. A000720, A001358, A066265, A064911.
%Y A072000 Sequence in context: A029131 A162351 A087816 this_sequence A157477 A006949 
               A055748
%Y A072000 Adjacent sequences: A071997 A071998 A071999 this_sequence A072001 A072002 
               A072003
%K A072000 easy,nonn
%O A072000 1,6
%A A072000 Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 19 2002
%E A072000 Edited by Robert G. Wilson v, Feb 15 2006