

A120037


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


8



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



