A120037 Number of 6-almost primes 6ap such that 2^n < 6ap <= 2^(n+1).

0, 0, 0, 0, 0, 1, 1, 5, 8, 22, 44, 96, 215, 439, 959, 1967, 4185, 8735, 18143, 37695, 77939, 161479, 332008, 684502, 1404867, 2882712, 5904454, 12078654, 24682057, 50375102, 102724466, 209250102, 425921989, 866187909, 1760280404, 3574740094

Offset

0,8

Comments

The partial sum equals the number of Pi_6(2^n).

Links

Table of n, a(n) for n=0..35.

Example

(2^6, 2^7] there is one semiprime, namely 96. 64 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[6, 2^n], {n, 0, 30}]; Rest@t - Most@t

Crossrefs

Cf. A046306, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.

Sequence in context: A140419 A292851 A138023 * A120038 A120039 A120040

Adjacent sequences: A120034 A120035 A120036 * A120038 A120039 A120040

Keyword

nonn

Author

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

Status

approved