A125527 Number of semiprimes <= 2^n.

0, 1, 2, 6, 10, 22, 42, 82, 157, 304, 589, 1124, 2186, 4192, 8110, 15658, 30253, 58546, 113307, 219759, 426180, 827702, 1608668, 3129211, 6091437, 11868599, 23140878, 45150717, 88157689, 172235073, 336717854, 658662065, 1289149627, 2524532330

Offset: 1

Author

Robert G. Wilson v, Dec 29 2006

Keywords

• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..63 (using data from A120033, terms n=48, 50..57 from Dana Jacobsen)
• Eric Weisstein's World of Mathematics, Semiprime.

Crossrefs

Cf. A126279, A066265, A007053, A120033, A127396.

Programs

Mathematica

SemiPrimePi[n_] := Sum[ PrimePi[ n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; Table[ SemiPrimePi[2^n], {n, 47}]

PARI

a(n)=my(s,i,N=2^n); forprime(p=2, sqrtint(N), s+=primepi(N\p); i++); s - i * (i-1)/2 \\ Charles R Greathouse IV, May 12 2013

Perl

use ntheory ":all"; print "$ ",semiprime_count(1 << $),"\n" for 1..48; # Dana Jacobsen, Sep 10 2018

Formula

a(n) = A072000(2^n). - R. J. Mathar, Aug 26 2011