A175613 - OEIS

%I #28 Jul 23 2024 18:13:24

%S 1,2,10,42,589,2186,30253,113307,1608668,88157689,336717854,

%T 19015826478,282528883551,1091574618496,16360940729894

%N Number of semiprimes <= 2^prime(n).

%F a(n) = A072000(A034785(n)) = A125527(A000040(n)). - _R. J. Mathar_, Dec 10 2010

%e a(2)=2 because first 2 semiprimes are 4, 6 both <2^prime(2)=8.

%t (* First run program given in A072000 to define the SemiPrimePi function *) Table[SemiPrimePi[2^Prime[n]], {n, 10}](* _Alonso del Arte_, Dec 10 2010 *)

%o (PARI) a(n)=my(N=2^prime(n),s,i); forprime(p=2, sqrtint(N), s+=primepi(N\p); i++); s - i * (i-1)/2 \\ _Charles R Greathouse IV_, Apr 25 2016

%o (Python)

%o from math import isqrt

%o from sympy import prime, primepi

%o def A175613(n):

%o     m = 1<<prime(n)

%o     return int(sum(primepi(m//prime(k))-k+1 for k in range(1,primepi(isqrt(m))+1))) # _Chai Wah Wu_, Jul 23 2024

%Y Cf. A001358, A007053, a proper subset of A125527.

%K nonn,less

%O 1,2

%A _Juri-Stepan Gerasimov_, Dec 04 2010

%E a(14) & a(15) from _Robert G. Wilson v_, Oct 19 2011.