login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A120038 Number of 7-almost primes 7ap such that 2^n < 7ap <= 2^(n+1). 8
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)