A120048 Number of 7-almost primes less than or equal to 10^n.

0, 0, 0, 14, 231, 2973, 35585, 409849, 4600247, 50678212, 550454756, 5913771637, 62981797962, 665997804082, 7001087934965, 73232029374751, 762783057783010, 7916319351632036, 81898808371556517

Offset: 0

Author

Robert G. Wilson v, Feb 07 2006

Keywords

• nonn

Examples

			There are 14 seven-almost primes up to 1000: 128, 192, 288, 320, 432, 448, 480, 648, 672, 704, 720, 800, 832 & 972.
		

Crossrefs

Cf. A066265, A014613, A116382.

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

Programs

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[7, 10^n], {n, 11}]

Extensions

More terms from Robert G. Wilson v, Jan 07 2007

Example corrected by Harvey P. Dale, Jan 25 2013

a(15)-a(18) from Henri Lifchitz, Mar 18 2025