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%I #7 Jul 06 2012 11:51:58
%S 0,0,0,0,0,0,0,1,1,5,8,22,47,101,229,473,1044,2171,4634,9796,20513,
%T 43020,89684,187361,388633,807508,1671160,3455934,7135226,14708436,
%U 30286472,62280024,127944070,262543635,538266791,1102507513,2256357137
%N Number of 8-almost primes 8ap such that 2^n < 8ap <= 2^(n+1).
%C The partial sum equals the number of Pi_8(2^n).
%e (2^8, 2^9] there is one semiprime, namely 384. 256 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[8, 2^n], {n, 0, 30}]; Rest@t - Most@t
%Y Cf. A046310, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.
%K nonn
%O 0,10
%A _Jonathan Vos Post_ and _Robert G. Wilson v_, Mar 21 2006
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