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!)
A120041 Number of 10-almost primes k such that 2^n < k <= 2^(n+1). 27
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 8, 22, 47, 103, 233, 487, 1072, 2246, 4803, 10202, 21440, 45115, 94434, 197891, 412010, 858846, 1783610, 3700698, 7665755, 15853990, 32750248, 67564405, 139238488, 286625278, 589472979, 1211146741, 2486322304 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

The partial sum equals the number of Pi_10(2^n).

LINKS

Table of n, a(n) for n=0..38.

FORMULA

a(n) ~ 2^n log^9 n/(725760 n log 2). [Charles R Greathouse IV, Dec 28 2011]

EXAMPLE

(2^10, 2^11] there is one semiprime, namely 1536. 1024 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[10, 2^n], {n, 0, 39}]; Rest@t - Most@t

CROSSREFS

Cf. A046314, A036378, A120033, A120034, A120035, A120036, A120037, A120038, A120039, A120040, A120041, A120042, A120043.

Sequence in context: A120038 A120039 A120040 * A120042 A120043 A063897

Adjacent sequences: A120038 A120039 A120040 * A120042 A120043 A120044

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.)