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A124033 Number of  n-digit numbers having exactly n prime factors (counted with multiplicity). 2
4, 31, 225, 1563, 10222, 63030, 374264, 2160300, 12196405, 67724342, 371233523, 2014305995, 10841722966, 57974736592, 308361428628, 1632877406997 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Essentially the same as A036335.

What would be the ratio between a(n) and all possible numbers with n digits for each n?

LINKS

Table of n, a(n) for n=1..16.

EXAMPLE

a(1) = A006880(1) = 4.

a(2) = A066265(2) - A066265(1) = 34 - 3 = 31.

a(3) = A109251(3) - A109251(2) = 247 - 22 = 225.

a(4) = A114106(4) - A114106(3) = 1712 - 149 = 1563.

a(5) = A114453(5) - A114453(4) = 11185 - 963 = 10222.

a(6) = A120047(6) - A120047(5) = 68963 - 5933 = 63030.

a(7) = A120048(7) - A120048(6) = 409849 - 35585 = 374264.

a(8) = A120049(8) - A120049(7) = 2367507 - 207207 = 2160300.

a(9) = A120050(9) - A120050(8) = 13377156 - 1180751 = 12196405.

a(10) = A120051(10) - A120051(9) = 74342563 - 6618221 = 67724342.

a(11) = A120052(11) - A120052(10) = 407818620 - 36585097 = 371233523.

a(12) = A120053(12) - A120053(11) = 2214357712 - 200051717 = 2014305995.

MATHEMATICA

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 *)

CROSSREFS

Sequence in context: A298996 A299663 A005216 * A014537 A136284 A183911

Adjacent sequences:  A124030 A124031 A124032 * A124034 A124035 A124036

KEYWORD

nonn,base

AUTHOR

J. M. Bergot, Apr 08 2011

EXTENSIONS

Corrected and extended by Ray Chandler, Apr 11 2011

a(9)-a(12) from Ray Chandler, Apr 12 2011

a(13)-a(16) from Robert G. Wilson v, Jul 06 2012

STATUS

approved

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Last modified August 18 13:25 EDT 2019. Contains 326100 sequences. (Running on oeis4.)