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A116430
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The number of n-almost primes less than or equal to 10^n, starting with a(0)=1.
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16
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1, 4, 34, 247, 1712, 11185, 68963, 409849, 2367507, 13377156, 74342563, 407818620, 2214357712, 11926066887, 63809981451, 339576381990, 1799025041767
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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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 (eww(AT)wolfram.com) Feb 07 2006 *)
Table[ AlmostPrimePi[n, 10^n], {n, 0, 13}]
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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, A120048, A120049, A120050, A120051, A120052, A120053, A116430.
Sequence in context: A085695 A049293 A198687 * A201684 A155628 A036352
Adjacent sequences: A116427 A116428 A116429 * A116431 A116432 A116433
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 10 2006, Jun 01 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 08 2008 at the suggestion of R. J. Mathar
a(15)-a(16) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 01 2010
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