|
%I #30 Apr 08 2022 11:11:13
%S 0,1,2,6,10,22,42,82,157,304,589,1124,2186,4192,8110,15658,30253,
%T 58546,113307,219759,426180,827702,1608668,3129211,6091437,11868599,
%U 23140878,45150717,88157689,172235073,336717854,658662065,1289149627,2524532330
%N Number of semiprimes <= 2^n.
%H Robert G. Wilson v, <a href="/A125527/b125527.txt">Table of n, a(n) for n = 1..63</a> (using data from A120033, terms n=48, 50..57 from Dana Jacobsen)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>.
%F a(n) = A072000(2^n). - _R. J. Mathar_, Aug 26 2011
%t SemiPrimePi[n_] := Sum[ PrimePi[ n/Prime@i] - i + 1, {i, PrimePi@ Sqrt@n}]; Table[ SemiPrimePi[2^n], {n, 47}]
%o (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
%o (Perl) use ntheory ":all"; print "$_ ",semiprime_count(1 << $_),"\n" for 1..48; # _Dana Jacobsen_, Sep 10 2018
%Y Cf. A126279, A066265, A007053, A120033, A127396.
%K nonn
%O 1,3
%A _Robert G. Wilson v_, Dec 29 2006
|
