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A120049
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Number of 8-almost primes less than or equal to 10^n.
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13
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0, 0, 0, 7, 105, 1418, 17572, 207207, 2367507, 26483012, 291646797, 3173159326, 34192782745, 365561221293, 3882841742380
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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EXAMPLE
| There are 2 eight-almost primes up to 1000: 256, 384, 576, 640, 864, 896 & 960.
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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[8, 10^n], {n, 12}]
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CROSSREFS
| Cf. A066265, A014613, A116382.
Cf. A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053, A116430.
Sequence in context: A098362 A093741 A139742 * A067420 A131869 A132867
Adjacent sequences: A120046 A120047 A120048 * A120050 A120051 A120052
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 07 2006
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EXTENSIONS
| a(13) and a(14) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 07 2007
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