A120038 Number of 7-almost primes 7ap such that 2^n < 7ap <= 2^(n+1).

0, 0, 0, 0, 0, 0, 1, 1, 5, 8, 22, 46, 99, 224, 461, 1013, 2093, 4459, 9388, 19603, 40946, 85087, 177200, 366248, 758686, 1565038, 3226717, 6641105, 13648299, 28018956, 57445770, 117667693, 240751326, 492172466, 1005221914, 2051468099

Offset: 0

Author

Jonathan Vos Post and Robert G. Wilson v, Mar 21 2006

Keywords

• nonn

Comments

The partial sum equals the number of Pi_7(2^n).

Examples

			(2^7, 2^8] there is one semiprime, namely 192. 128 was counted in the previous entry.
		

Crossrefs

Cf. A046308, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.

Programs

Mathematica

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 = Table[AlmostPrimePi[7, 2^n], {n, 0, 30}]; Rest@t - Most@t