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%I #7 Jul 06 2012 11:51:27
%S 0,0,0,0,0,0,1,1,5,8,22,46,99,224,461,1013,2093,4459,9388,19603,40946,
%T 85087,177200,366248,758686,1565038,3226717,6641105,13648299,28018956,
%U 57445770,117667693,240751326,492172466,1005221914,2051468099
%N Number of 7-almost primes 7ap such that 2^n < 7ap <= 2^(n+1).
%C The partial sum equals the number of Pi_7(2^n).
%e (2^7, 2^8] there is one semiprime, namely 192. 128 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[7, 2^n], {n, 0, 30}]; Rest@t - Most@t
%Y Cf. A046308, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.
%K nonn
%O 0,9
%A _Jonathan Vos Post_ and _Robert G. Wilson v_, Mar 21 2006