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A120048
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Number of 7-almost primes less than or equal to 10^n.
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11
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0, 0, 0, 14, 231, 2973, 35585, 409849, 4600247, 50678212, 550454756, 5913771637, 62981797962, 665997804082, 7001087934965
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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EXAMPLE
| There are 7 seven-almost primes up to 100: 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832 & 972.
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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[7, 10^n], {n, 11}]
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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: A145269 A027774 A099272 * A079563 A166774 A055477
Adjacent sequences: A120045 A120046 A120047 * A120049 A120050 A120051
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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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