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

0,4

Links

Table of n, a(n) for n=0..18.

Example

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

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}]

Crossrefs

Cf. A066265, A014613, A116382.

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

Sequence in context: A027774 A099272 A273625 * A079563 A230346 A280559

Adjacent sequences: A120045 A120046 A120047 * A120049 A120050 A120051

Keyword

nonn

Author

Robert G. Wilson v, Feb 07 2006

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

Status

approved