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 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 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

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Last modified May 26 13:49 EDT 2020. Contains 334626 sequences. (Running on oeis4.)