A334069 Number of numbers <= 2^n that are the product of exactly four primes, not necessarily distinct.

0, 0, 0, 1, 2, 7, 14, 34, 71, 152, 325, 669, 1405, 2866, 5931, 12139, 24782, 50444, 102458, 207945, 420511, 850518, 1716168, 3460304, 6968639, 14022029, 28189833, 56631732, 113697179, 228115641, 457456902, 916899721, 1836996851, 3678943569, 7365141297, 14740076678, 29490954290

Offset

1,5

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..53

Eric Weisstein's World of Mathematics, Almost Prime.

Eric Weisstein's World of Mathematics, Semiprime.

Formula

a(n) = A082996(2^n).

Example

a(6) = 7 because
  16 = 2 * 2 * 2 * 2,
  24 = 2 * 2 * 2 * 3,
  36 = 2 * 2 * 3 * 3,
  40 = 2 * 2 * 2 * 5,
  54 = 2 * 3 * 3 * 3,
  56 = 2 * 2 * 2 * 7, and
  60 = 2 * 2 * 3 * 5
are the seven numbers less than 2^6 = 64 that are each the product of four primes.

Mathematica

FourAlmostPrimePi[n_] := Sum[ PrimePi[n/(Prime@i*Prime@j*Prime@k)] - k + 1, {i, PrimePi[n^(1/4)]}, {j, i, PrimePi[(n/Prime@i)^(1/3)]}, {k, j, PrimePi@Sqrt[n/(Prime@i*Prime@j)]}]; Array[FourAlmostPrimePi[2^#] &, 37]

Crossrefs

Cf. A007053, A014613, A082996, A125527, A127396, A126279.

Partial sums of A120035.

Sequence in context: A286861 A290682 A000147 * A128902 A227213 A319455

Adjacent sequences: A334066 A334067 A334068 * A334070 A334071 A334072

Keyword

nonn

Author

Robert G. Wilson v, Apr 13 2020

Status

approved