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%I #10 Apr 14 2020 20:33:13
%S 0,0,0,1,1,5,7,20,37,81,173,344,736,1461,3065,6208,12643,25662,52014,
%T 105487,212566,430007,865650,1744136,3508335,7053390,14167804,
%U 28441899,57065447,114418462,229341261,459442819,920097130,1841946718,3686197728
%N Number of 4-almost primes f such that 2^n < f <= 2^(n+1).
%C The partial sum equals the number of Pi_4(2^n) = A334069(n).
%e (2^4, 2^5] there is one semiprime, namely 24. 16 was counted in the previous entry.
%t FourAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@Sqrt[n/(Prime@i*Prime@j)]}]; t = Table[ FourAlmostPrimePi[2^n], {n, 0, 37}]; Rest@t - Most@t
%Y Cf. A014613, A082996, A114106, A036378, A120033 - A120043, A334069.
%K nonn
%O 0,6
%A _Jonathan Vos Post_ and _Robert G. Wilson v_, Mar 20 2006
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