OFFSET
1,2
FORMULA
EXAMPLE
a(2)=2 because first 2 semiprimes are 4, 6 both <2^prime(2)=8.
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 *)
PROG
(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<<prime(n)
return int(sum(primepi(m//prime(k))-k+1 for k in range(1, primepi(isqrt(m))+1))) # Chai Wah Wu, Jul 23 2024
CROSSREFS
KEYWORD
nonn,less
AUTHOR
Juri-Stepan Gerasimov, Dec 04 2010
EXTENSIONS
a(14) & a(15) from Robert G. Wilson v, Oct 19 2011.
STATUS
approved