A120043 Number of 12-almost primes 12ap such that 2^n < 12ap <= 2^(n+1).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 8, 22, 47, 103, 234, 492, 1082, 2271, 4867, 10349, 21794, 45907, 96293, 202006, 421287, 879388, 1828931, 3800227, 7882784, 16325796, 33771056, 69767214, 143971956, 296771231, 611156696, 1257374970

Offset

0,14

Comments

The partial sum equals the number of Pi_12(2^n).

Links

Table of n, a(n) for n=0..39.

Example

(2^12, 2^13] there is one semiprime, namely 6144. 4096 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[12, 2^n], {n, 0, 30}]; Rest@t - Most@t

Crossrefs

Cf. A069273, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.

Sequence in context: A120040 A120041 A120042 * A063897 A092733 A116884

Adjacent sequences: A120040 A120041 A120042 * A120044 A120045 A120046

Keyword

nonn

Author

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

Status

approved