login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A125288 a(n) = number of integers k such that for all integers greater than k, 2*Pi(n,k) is always greater than Pi(n,2*k). 0
10, 297, 49650, 180701087317 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Pi(m, n) is the number of integers less than or equal to n which has m prime factors counting multiplicity, also known as k-almost primes (A078840).

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

a(1) = 10 since there are now 4 primes {2, 3, 5 & 7} and 4 semiprimes {4, 6, 9 & 10} less than or equal to 10.

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 *)

CROSSREFS

Cf. A126279, A125149, A092097.

Sequence in context: A239775 A059072 A000459 * A217487 A173479 A173478

Adjacent sequences:  A125285 A125286 A125287 * A125289 A125290 A125291

KEYWORD

more,nonn

AUTHOR

Jonathan Vos Post and Robert G. Wilson v, Jan 22 2007

EXTENSIONS

a(4) from Donovan Johnson, Nov 13 2010

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 20 05:29 EDT 2019. Contains 321344 sequences. (Running on oeis4.)