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

0,10

Comments

The partial sum equals the number of Pi_8(2^n).

Links

Table of n, a(n) for n=0..36.

Example

(2^8, 2^9] there is one semiprime, namely 384. 256 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[8, 2^n], {n, 0, 30}]; Rest@t - Most@t

Crossrefs

Cf. A046310, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.

Sequence in context: A138023 A120037 A120038 * A120040 A120041 A120042

Adjacent sequences: A120036 A120037 A120038 * A120040 A120041 A120042

Keyword

nonn

Author

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

Status

approved