%I #7 Jul 06 2012 11:50:57
%S 0,0,0,0,0,1,1,5,8,22,44,96,215,439,959,1967,4185,8735,18143,37695,
%T 77939,161479,332008,684502,1404867,2882712,5904454,12078654,24682057,
%U 50375102,102724466,209250102,425921989,866187909,1760280404,3574740094
%N Number of 6-almost primes 6ap such that 2^n < 6ap <= 2^(n+1).
%C The partial sum equals the number of Pi_6(2^n).
%e (2^6, 2^7] there is one semiprime, namely 96. 64 was counted in the previous entry.
%t AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]]]]]; (* _Eric W. Weisstein_, Feb 07 2006 *)
%t t = Table[AlmostPrimePi[6, 2^n], {n, 0, 30}]; Rest@t - Most@t
%Y Cf. A046306, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.
%K nonn
%O 0,8
%A _Jonathan Vos Post_ and _Robert G. Wilson v_, Mar 21 2006