A120034 Number of 3-almost primes t such that 2^n < t <= 2^(n+1).

0, 0, 1, 1, 5, 6, 17, 30, 65, 131, 257, 536, 1033, 2132, 4187, 8370, 16656, 33123, 65855, 130460, 259431, 513737, 1019223, 2019783, 4003071, 7930375, 15712418, 31126184, 61654062, 122137206, 241920724, 479226157, 949313939, 1880589368, 3725662783

Offset: 0

Author

Jonathan Vos Post and Robert G. Wilson v, Mar 20 2006

Keywords

• nonn

Comments

The partial sum equals the number of Pi_3(2^n) = A127396(n).

Examples

			(2^3, 2^4] there is one semiprime, namely 12. 8 was counted in the previous entry.
		

Crossrefs

Cf. A014612, A072114, A109251, A036378, A120033 - A120043.

Programs

Mathematica

ThreeAlmostPrimePi[n_] := Sum[PrimePi[n/(Prime@i*Prime@j)] - j + 1, {i, PrimePi[n^(1/3)]}, {j, i, PrimePi@Sqrt[n/Prime@i]}]; t = Table[ ThreePrimePi[2^n], {n, 0, 35}]; Rest@t - Most@t