A175613 Number of semiprimes <= 2^prime(n).

1, 2, 10, 42, 589, 2186, 30253, 113307, 1608668, 88157689, 336717854, 19015826478, 282528883551, 1091574618496, 16360940729894

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 04 2010

Keywords

• nonn
• less

Examples

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

Crossrefs

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

Programs

Mathematica

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

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

Python

from math import isqrt
from sympy import prime, primepi
def A175613(n):
    m = 1<Chai Wah Wu, Jul 23 2024

Formula

a(n) = A072000(A034785(n)) = A125527(A000040(n)). - R. J. Mathar, Dec 10 2010

Extensions

a(14) & a(15) from Robert G. Wilson v, Oct 19 2011.