A120050 Number of 9-almost primes less than or equal to 10^n.

0, 0, 0, 2, 47, 671, 8491, 101787, 1180751, 13377156, 148930536, 1636170477, 17787688377, 191742524399, 2052389350029

Offset

0,4

Links

Table of n, a(n) for n=0..14.

Example

There are 2 nine-almost primes up to 1000: 512 & 768.

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, Feb 07 2006 *)
Table[AlmostPrimePi[9, 10^n], {n, 12}]

Crossrefs

Cf. A066265, A014613, A116382.

Cf. A006880, A036352, A109251, A114106, A114453, A120047, A120048, A120049, A120050, A120051, A120052, A120053, A116430.

Sequence in context: A226420 A160922 A276509 * A112783 A277655 A246543

Adjacent sequences: A120047 A120048 A120049 * A120051 A120052 A120053

Keyword

nonn

Author

Robert G. Wilson v, Feb 07 2006

Extensions

a(13) and a(14) from Robert G. Wilson v, Jan 07 2007

Status

approved