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%I #11 May 13 2013 01:48:38
%S 0,0,0,0,0,0,0,0,0,1,1,5,8,22,47,103,233,487,1072,2246,4803,10202,
%T 21440,45115,94434,197891,412010,858846,1783610,3700698,7665755,
%U 15853990,32750248,67564405,139238488,286625278,589472979,1211146741,2486322304
%N Number of 10-almost primes k such that 2^n < k <= 2^(n+1).
%C The partial sum equals the number of Pi_10(2^n).
%F a(n) ~ 2^n log^9 n/(725760 n log 2). [_Charles R Greathouse IV_, Dec 28 2011]
%e (2^10, 2^11] there is one semiprime, namely 1536. 1024 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[10, 2^n], {n, 0, 39}]; Rest@t - Most@t
%Y Cf. A046314, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.
%K nonn
%O 0,12
%A _Jonathan Vos Post_ and _Robert G. Wilson v_, Mar 21 2006
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