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A120051
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Number of 10-almost primes less than or equal to 10^n.
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11
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0, 0, 0, 0, 22, 306, 4016, 49163, 578154, 6618221, 74342563, 823164388, 9011965866, 97765974368, 1052666075366
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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EXAMPLE
| There are 22 ten-almost primes up to 10000: 1024, 1536, 2304, 2560, 3456, 3584, 3840, 5184, 5376, 5632, 5760, 6400, 6656, 7776, 8064, 8448, 8640, 8704, 8960, 9600, 9728 & 9984.
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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[10, 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: A088279 A028109 A003468 * A041928 A028054 A100789
Adjacent sequences: A120048 A120049 A120050 * A120052 A120053 A120054
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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
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 07 2007
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