A120040 Number of 9-almost primes 9ap such that 2^n < 9ap <= 2^(n+1).

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 8, 22, 47, 102, 232, 482, 1062, 2217, 4738, 10051, 21083, 44315, 92608, 193824, 402936, 838879, 1739794, 3605077, 7457977, 15404202, 31781036, 65481376, 134777594, 277096118, 569173839, 1168002568, 2394834166

Offset

0,11

Comments

The partial sum equals the number of Pi_9(2^n).

Links

Table of n, a(n) for n=0..37.

Example

(2^9, 2^10] there is one semiprime, namely 768. 512 was counted in the previous entry.

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[9, 2^n], {n, 0, 30}]; Rest@t - Most@t

Crossrefs

Cf. A046312, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.

Sequence in context: A120037 A120038 A120039 * A120041 A120042 A120043

Adjacent sequences: A120037 A120038 A120039 * A120041 A120042 A120043

Keyword

nonn

Author

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

Status

approved