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

0,9

Comments

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

Links

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

Example

(2^7, 2^8] there is one semiprime, namely 192. 128 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[7, 2^n], {n, 0, 30}]; Rest@t - Most@t

Crossrefs

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

Sequence in context: A292851 A138023 A120037 * A120039 A120040 A120041

Adjacent sequences: A120035 A120036 A120037 * A120039 A120040 A120041

Keyword

nonn

Author

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

Status

approved