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A124033
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Number of n-digit numbers having exactly n prime factors (counted with multiplicity).
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2
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4, 31, 225, 1563, 10222, 63030, 374264, 2160300, 12196405, 67724342, 371233523, 2014305995, 10841722966, 57974736592, 308361428628, 1632877406997
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OFFSET
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1,1
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COMMENTS
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What would be the ratio between a(n) and all possible numbers with n digits for each n?
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LINKS
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EXAMPLE
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a(12) = A120053(12) - A120053(11) = 2214357712 - 200051717 = 2014305995.
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MATHEMATICA
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Table[Count[Range[10^(n-1), 10^n-1], _?(PrimeOmega[#]==n&)], {n, 8}] (* Harvey P. Dale, Apr 22 2011 *)
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 *)
f[n_] := AlmostPrimePi[n, 10^n - 1] - AlmostPrimePi[n, 10^(n - 1) - 1]; Array[f, 12] (* Robert G. Wilson v, Jul 06 2012 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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