

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




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 kalmost 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



