This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A175613 #28 Jul 23 2024 18:13:24
%S A175613 1,2,10,42,589,2186,30253,113307,1608668,88157689,336717854,
%T A175613 19015826478,282528883551,1091574618496,16360940729894
%N A175613 Number of semiprimes <= 2^prime(n).
%F A175613 a(n) = A072000(A034785(n)) = A125527(A000040(n)). - _R. J. Mathar_, Dec 10 2010
%e A175613 a(2)=2 because first 2 semiprimes are 4, 6 both <2^prime(2)=8.
%t A175613 (* 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 A175613 (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 A175613 (Python)
%o A175613 from math import isqrt
%o A175613 from sympy import prime, primepi
%o A175613 def A175613(n):
%o A175613 m = 1<<prime(n)
%o A175613 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 A175613 Cf. A001358, A007053, a proper subset of A125527.
%K A175613 nonn,less
%O A175613 1,2
%A A175613 _Juri-Stepan Gerasimov_, Dec 04 2010
%E A175613 a(14) & a(15) from _Robert G. Wilson v_, Oct 19 2011.