A120039 Number of 8-almost primes 8ap such that 2^n < 8ap <= 2^(n+1).

0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 8, 22, 47, 101, 229, 473, 1044, 2171, 4634, 9796, 20513, 43020, 89684, 187361, 388633, 807508, 1671160, 3455934, 7135226, 14708436, 30286472, 62280024, 127944070, 262543635, 538266791, 1102507513, 2256357137

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_8(2^n).

Examples

			(2^8, 2^9] there is one semiprime, namely 384. 256 was counted in the previous entry.
		

Crossrefs

Cf. A046310, 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[8, 2^n], {n, 0, 30}]; Rest@t - Most@t