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A175613
Number of semiprimes <= 2^prime(n).
1
1, 2, 10, 42, 589, 2186, 30253, 113307, 1608668, 88157689, 336717854, 19015826478, 282528883551, 1091574618496, 16360940729894
OFFSET
1,2
FORMULA
a(n) = A072000(A034785(n)) = A125527(A000040(n)). - R. J. Mathar, Dec 10 2010
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
Cf. A001358, A007053, a proper subset of A125527.
Sequence in context: A119694 A286760 A197048 * A296001 A121949 A376225
KEYWORD
nonn,less
AUTHOR
EXTENSIONS
a(14) & a(15) from Robert G. Wilson v, Oct 19 2011.
STATUS
approved