almost primes

[N. J. A. Sloane]

> What is the asymptotics for the number of products of 2 primes not
> exceeding x?

Answer from entry A072000 in the OEIS:

%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.
%C A072000 Let A be a positive integer then card{ x <= n : bigomega(x) = A } ~ (n/Log(n))*Log(
Log(n))^(A-1)/(A-1)!
%D A072000 G. Tenenbaum, Introduction \`a la th\'eorie analytique et probabiliste des nombres,
 p. 203, Publications de l'Institut Cartan, 1990.
%H A072000 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semipr
ime.html">Semiprime</a>
%F A072000 a(n) = Sum_{i=1..Pi(sqrt(n))} Pi(n/P_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).
%t A072000 SemiPrimePi[n_] := Sum[ PrimePi[n/Prime at i] -i + 1, {i, PrimePi at Sqrt@n}]; Array[Semi
PrimePi, 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.
%K A072000 easy,nonn
%O A072000 1,6
%A A072000 Benoit Cloitre (abmt(AT)wanadoo.fr), Jun 19 2002
%E A072000 Edited by Robert G. Wilson v, Feb 15 2006

I think the asymptotic formula was provided by Robert Wilson

Neil Sloane