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

Author

Robert G. Wilson v, Apr 13 2020

Keywords

• nonn

Examples

			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.
		

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.

Crossrefs

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

Partial sums of A120035.

Programs

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]

Formula

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