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A116430 The number of n-almost primes less than or equal to 10^n, starting with a(0)=1. 16
1, 4, 34, 247, 1712, 11185, 68963, 409849, 2367507, 13377156, 74342563, 407818620, 2214357712, 11926066887, 63809981451, 339576381990, 1799025041767 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If instead we asked for those less than or equal to 2^n, then the sequence is A000012: The simplest sequence of positive numbers: the all 1's sequence.

LINKS

Table of n, a(n) for n=0..16.

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 *)

Table[ AlmostPrimePi[n, 10^n], {n, 0, 13}]

CROSSREFS

Cf. A036352, A114106, A114453.

Cf. A078840, A078841, A078842, A116432, A078843, A116426, A078844, A116427, A078845, A116428, A116429, A116430, A078846, A116431.

Cf. A006880, A036352, A109251, A114106, A114453, A120047 - A120053.

Sequence in context: A085695 A049293 A198687 * A216239 A335667 A201684

Adjacent sequences:  A116427 A116428 A116429 * A116431 A116432 A116433

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Feb 10 2006, Jun 01 2006

EXTENSIONS

Edited by N. J. A. Sloane, Aug 08 2008 at the suggestion of R. J. Mathar

a(15)-a(16) from Donovan Johnson, Oct 01 2010

STATUS

approved

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Last modified May 9 19:28 EDT 2021. Contains 343746 sequences. (Running on oeis4.)